Receiving apparatus and de-interleaving method thereof

ABSTRACT

A transmitting apparatus and a receiving apparatus are provided. The transmitting apparatus includes: an encoder configured to generate a low density parity check (LDPC) codeword by LDPC encoding based on a parity check matrix; an interleaver configured to interleave the LDPC codeword; and a modulator configured to map the interleaved LDPC codeword onto a modulation symbol, wherein the modulator is further configured to map a bit included in a predetermined bit group from among a plurality of bit groups constituting the LDPC codeword onto a predetermined bit of the modulation symbol.

CROSS-REFERENCE TO THE RELATED APPLICATIONS

This is a continuation of U.S. patent application Ser. No. 15/435,042, filed Feb. 16, 2017, which is a continuation of U.S. patent application Ser. No. 15/130,204, filed on Apr. 15, 2016, issued as U.S. Pat. No. 9,692,454 on Jun. 27, 2017, which is a continuation of U.S. patent application Ser. No. 14/625,862, filed Feb. 19, 2015, issued as U.S. Pat. No. 9,602,137 on Mar. 21, 2017, which claims priority from U.S. Provisional Application No. 61/941,676 filed on Feb. 19, 2014, U.S. Provisional Application No. 62/001,170 filed on May 21, 2014, and Korean Patent Application No. 10-2015-0000671 filed on Jan. 5, 2015. The entire disclosures of the prior applications are considered part of the disclosure of this continuation application, and are hereby incorporated by reference.

BACKGROUND

1. Technical Field

Apparatuses and methods consistent with exemplary embodiments relate to a transmitting apparatus and an interleaving method thereof, and more particularly, to a transmitting apparatus which processes data and transmits the data, and an interleaving method thereof.

2. Description of the Related Art

In the 21st century information-oriented society, broadcasting communication services are moving into the era of digitalization, multi-channel, wideband, and high quality. In particular, as high quality digital televisions and portable multimedia player and portable broadcasting equipments are increasingly used in recent years, there is an increasing demand for methods for supporting various receiving methods of digital broadcasting services.

In order to meet such demand, standard groups are establishing various standards and are providing a variety of services to satisfy users' needs. Therefore, there is a need for a method for providing improved services to users with high decoding and receiving performance.

SUMMARY

Exemplary embodiments may overcome the above disadvantages and other disadvantages not described above. However, it is understood that the exemplary embodiment are not required to overcome the disadvantages described above, and may not overcome any of the problems described above.

The exemplary embodiments provide a transmitting apparatus which can map a bit included in a predetermined bit group from among a plurality of bit groups of a low density parity check (LDPC) codeword onto a predetermined bit of a modulation symbol, and transmit the bit, and an interleaving method thereof.

According to an aspect of an exemplary embodiment, there is provided a transmitting apparatus which may include: an encoder configured to generate an LDPC codeword by LDPC encoding based on a parity check matrix; an interleaver configured to interleave the LDPC codeword; and a modulator configured to map the interleaved LDPC codeword onto a modulation symbol, wherein the modulator is further configured to map a bit included in a predetermined bit group from among a plurality of bit groups constituting the LDPC codeword onto a predetermined bit of the modulation symbol.

Each of the plurality of bit groups may be formed of M number of bits, and M may be a common divisor of N_(ldpc) and K_(ldpc) and may be determined to satisfy Q_(ldpc)=(N_(ldpc)−K_(ldpc))/M. Q_(ldpc) is a cyclic shift parameter value regarding columns in a column group of an information word submatrix of the parity check matrix, N_(ldpc) is a length of the LDPC codeword, and K_(ldpc) is a length of information word bits of the LDPC codeword.

The interleaver may include: a parity interleaver configured to interleave parity bits of the LDPC codeword; a group interleaver configured to divide the parity-interleaved LDPC codeword by the plurality of bit groups and rearrange an order of the plurality of bit groups in bit group wise; and a block interleaver configured to interleave the plurality of bit groups the order of which is rearranged.

The group interleaver may be configured to rearrange the order of the plurality of bit groups in bit group wise based on Equation 21.

π(j) in Equation 21 may be determined based on at least one of a length of the LDPC codeword, a modulation method, and a code rate.

When the LDPC codeword has a length of 16200, the modulation method is QPSK, and the code rate is 13/15, π(j) in Equation 21 may be defined as in Table 36.

The interleaver may include: a group interleaver configured to divide the LDPC codeword into the plurality of bit groups and rearrange an order of the plurality of bit groups in bit group wise; and a block interleaver configured to interleave the plurality of bit groups the order of which is rearranged.

The group interleaver may be configured to rearrange the order of the plurality of bit groups in bit group wise based on Equation 21.

π(j) in Equation 21 may be determined based on at least one of a length of the LDPC codeword, a modulation method, and a code rate.

When the LDPC codeword has a length of 16200, the modulation method is QPSK, and the code rate is 5/15, π(j) in Equation 21 is defined as in Table 32.

The block interleaver may be configured to interleave by writing the plurality of bit groups in each of a plurality of columns in bit group wise in a column direction, and reading each row of the plurality of columns in which the plurality of bit groups are written in bit group wise in a row direction.

The block interleaver may be configured to serially write, in the plurality of columns, at least some bit groups which are writable in the plurality of columns in bit group wise from among the plurality of bit groups, and then divide and write the other bit groups in an area which remains after the at least some bit groups are written in the plurality of columns in bit group wise.

According to an aspect of another exemplary embodiment, there is provided an interleaving method of a transmitting apparatus. The method may include: generating an LDPC codeword by LDPC encoding based on a parity check matrix; interleaving the LDPC codeword; and mapping the interleaved LDPC codeword onto a modulation symbol, wherein the mapping includes mapping a bit included in a predetermined bit group from among a plurality of bit groups constituting the LDPC codeword onto a predetermined bit of the modulation symbol.

Each of the plurality of bit groups may be formed of M number of bits, and M may be a common divisor of N_(ldpc) and K_(ldpc) and may be determined to satisfy Q_(ldpc)=(N_(ldpc)−K_(ldpc))/M. Q_(ldpc) is a cyclic shift parameter value regarding columns in a column group of an information word submatrix of the parity check matrix, N_(ldpc) is a length of the LDPC codeword, and K_(ldpc) is a length of information word bits of the LDPC codeword.

The interleaving may include: interleaving parity bits of the LDPC codeword; dividing the parity-interleaved LDPC codeword by the plurality of bit groups and rearranging an order of the plurality of bit groups in bit group wise; and interleaving the plurality of bit groups the order of which is rearranged.

The rearranging in bit group wise may include rearranging the order of the plurality of bit groups in bit group wise based on Equation 21.

π(j) in Equation 21 may be determined based on at least one of a length of the LDPC codeword, a modulation method, and a code rate.

When the LDPC codeword has a length of 16200, the modulation method is QPSK, and the code rate is 13/15, π(j) in Equation 21 may be defined as in Table 36.

The interleaving may include: dividing the interleaved LDPC codeword into the plurality of bit groups and rearranging an order of the plurality of bit groups in bit group wise; and interleaving the plurality of bit groups the order of which is rearranged.

The rearranging in bit group wise may include rearranging the order of the plurality of bit groups in bit group wise based on Equation 21.

π(j) in Equation 21 may be determined based on at least one of a length of the LDPC codeword, a modulation method, and a code rate.

When the LDPC codeword has a length of 16200, the modulation method is QPSK, and the code rate is 5/15, π(j) in Equation 21 may be defined as in Table 32.

The interleaving the plurality of bit groups may include interleaving by writing the plurality of bit groups in each of a plurality of columns in bit group wise in a column direction, and reading each row of the plurality of columns in which the plurality of bit groups are written in bit group wise in a row direction.

The interleaving the plurality of bit groups may include serially writing, in the plurality of columns, at least some bit groups which are writable in the plurality of columns in bit group wise from among the plurality of bit groups, and then dividing and writing the other bit groups in an area which remains after the at least some bit groups are written in the plurality of columns in bit group wise.

According to various exemplary embodiments, improved decoding and receiving performance can be provided.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and/or other aspects will be more apparent by describing in detail exemplary embodiments, with reference to the accompanying drawings, in which:

FIG. 1 is a block diagram to illustrate a configuration of a transmitting apparatus according to an exemplary embodiment;

FIGS. 2 to 4 illustrate a configuration of a parity check matrix according to various exemplary embodiments;

FIG. 5 is a block diagram to illustrate a configuration of an interleaver according to an exemplary embodiment;

FIGS. 6 to 8 illustrate an interleaving method according to exemplary embodiments;

FIGS. 9 to 15 illustrate an interleaving method of a block interleaver according to exemplary embodiments;

FIG. 16 illustrates an operation of a demultiplexer according to an exemplary embodiment;

FIGS. 17 to 19 illustrate a method for extracting interleaving parameters according to exemplary embodiments;

FIG. 20 is a block diagram to illustrate a configuration of a receiving apparatus according to an exemplary embodiment;

FIG. 21 is a block diagram to illustrate a configuration of a deinterleaver according to an exemplary embodiment;

FIG. 22 illustrates a deinterleaving method of a block deinterleaver according to an exemplary embodiment; and

FIG. 23 is a flowchart to illustrate an interleaving method according to an exemplary embodiment.

DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS

Hereinafter, various exemplary embodiments will be described in greater detail with reference to the accompanying drawings.

In the following description, same reference numerals are used for the same elements when they are depicted in different drawings. The matters defined in the description, such as detailed construction and elements, are provided to assist in a comprehensive understanding of the exemplary embodiments. Thus, it is apparent that the exemplary embodiments can be carried out without those specifically defined matters. Also, functions or elements known in the related art are not described in detail since they would obscure the exemplary embodiments with unnecessary detail.

FIG. 1 is a block diagram to illustrate a configuration of a transmitting apparatus according to an exemplary embodiment. Referring to FIG. 1, the transmitting apparatus 100 includes an encoder 110, an interleaver 120, and a modulator 130 (or a constellation mapper).

The encoder 110 generates a low density parity check (LDPC) codeword by performing LDPC encoding based on a parity check matrix. To achieve this, the encoder 110 may include an LDPC encoder (not shown) to perform the LDPC encoding.

Specifically, the encoder 110 LDPC-encodes information word (or information) bits to generate the LDPC codeword which is formed of the information word bits and parity bits (that is, LDPC parity bits). Here, bits input to the encoder 110 may be used to the information word bits. Also, since an LDPC code is a systematic code, the information word bits may be included in the LDPC codeword as they are.

The LDPC codeword is formed of the information word bits and the parity bits. For example, the LDPC codeword is formed of N_(ldpc) number of bits, and includes K_(ldpc) number of information word bits and N_(parity)=N_(ldpc)−K_(ldpc) number of parity bits.

In this case, the encoder 110 may generate the LDPC codeword by performing the LDPC encoding based on the parity check matrix. That is, since the LDPC encoding is a process for generating an LDPC codeword to satisfy H·C^(T)=0, the encoder 110 may use the parity check matrix when performing the LDPC encoding. Herein, H is a parity check matrix and C is an LDPC codeword.

For the LDPC encoding, the transmitting apparatus 100 may include a memory and may pre-store parity check matrices of various formats.

For example, the transmitting apparatus 100 may pre-store parity check matrices which are defined in Digital Video Broadcasting-Cable version 2 (DVB-C2), Digital Video Broadcasting-Satellite-Second Generation (DVB-S2), Digital Video Broadcasting-Second Generation Terrestrial (DVB-T2), etc., or may pre-store parity check matrices which are defined in the North America digital broadcasting standard system Advanced Television System Committee (ATSC) 3.0 standards, which are currently being established. However, this is merely an example and the transmitting apparatus 100 may pre-store parity check matrices of other formats in addition to these parity check matrices.

Hereinafter, a parity check matrix according to various exemplary embodiments will be explained in detail with reference to the drawings. In the parity check matrix, elements other than elements having 1 have 0.

For example, the parity check matrix according to an exemplary embodiment may have a configuration of FIG. 2.

Referring to FIG. 2, a parity check matrix 200 is formed of an information word submatrix (or an information submatrix) 210 corresponding to information word bits, and a parity submatrix 220 corresponding to parity bits.

The information word submatrix 210 includes K_(ldpc) number of columns and the parity submatrix 220 includes N_(parity)=N_(ldpc)−K_(ldpc) number of columns. The number of rows of the parity check matrix 200 is identical to the number of columns of the parity submatrix 220, N_(parity)=N_(ldpc)−K_(ldpc).

In addition, in the parity check matrix 200, N_(ldpc) is a length of an LDPC codeword, K_(ldpc) is a length of information word bits, and N_(parity)=N_(ldpc)−K_(ldpc) is a length of parity bits. The length of the LDPC codeword, the information word bits, and the parity bits mean the number of bits included in each of the LDPC codeword, the information word bits, and the parity bits.

Hereinafter, the configuration of the information word submatrix 210 and the parity submatrix 220 will be explained in detail.

The information word submatrix 210 includes K_(ldpc) number of columns (that is, 0^(th) column to (K_(ldpc)−1)^(th) column), and follows the following rules:

First, M number of columns from among K_(ldpc) number of columns of the information word submatrix 210 belong to the same group, and K_(ldpc) number of columns is divided into K_(ldpc)/M number of column groups. In each column group, a column is cyclic-shifted from an immediately previous column by Q_(ldpc). That is, Q_(ldpc) may be a cyclic shift parameter value regarding columns in a column group of the information word submatrix 210 of the parity check matrix 200.

Herein, M is an interval at which a pattern of a column group, which includes a plurality of columns, is repeated in the information word submatrix 210 (e.g., M=360), and Q_(ldpc) is a size by which one column is cyclic-shifted from an immediately previous column in a same column group in the information word submatrix 210. Also, M is a common divisor of N_(ldpc) and K_(ldpc) and is determined to satisfy Q_(ldpc)=(N_(ldpc)−K_(ldpc))/M. Here, M and Q_(ldpc) are integers and K_(ldpc)/M is also an integer. M and Q_(ldpc) may have various values according to a length of the LDPC codeword and a code rate (CR)(or, coding rate).

For example, when M=360 and the length of the LDPC codeword, N_(ldpc), is 64800, Q_(ldpc) may be defined as in Table 1 presented below, and, when M=360 and the length N_(ldpc) of the LDPC codeword is 16200, Q_(ldpc) may be defined as in Table 2 presented below.

TABLE 1 Code Rate N_(ldpc) M Q_(ldpc)  5/15 64800 360 120  6/15 64800 360 108  7/15 64800 360 96  8/15 64800 360 84  9/15 64800 360 72 10/15 64800 360 60 11/15 64800 360 48 12/15 64800 360 36 13/15 64800 360 24

TABLE 2 Code Rate N_(ldpc) M Q_(ldpc)  5/15 16200 360 30  6/15 16200 360 27  7/15 16200 360 24  8/15 16200 360 21  9/15 16200 360 18 10/15 16200 360 15 11/15 16200 360 12 12/15 16200 360 9 13/15 16200 360 6

Second, when the degree of the 0^(th) column of the i^(th) column group (i=0, 1, . . . , K_(ldpc)/M−1) is D_(i) (herein, the degree is the number of value 1 existing in each column and all columns belonging to the same column group have the same degree), and a position (or an index) of each row where 1 exists in the 0^(th) column of the i^(th) column group is R_(i,0) ⁽⁰⁾,R_(i,0) ⁽¹⁾, . . . , R_(i,0) ^((D) ^(i) ⁻¹⁾, an index R_(i,j) ^((k)) of a row where k^(th) 1 is located in the j^(th) column in the i^(th) column group is determined by following Equation 1: R _(i,j) ^((k)) =R _(i,(j-1)) ^((k)) +Q _(ldpc) mod(N _(ldpc) −K _(ldpc))  (1), where k=0, 1, 2, . . . D₁−1; i=0, 1, . . . , K_(ldpc)/M−1; and j=1, 2, . . . , M−1.

Equation 1 can be expressed as following Equation 2: R _(i,j) ^((k)) ={R _(i,0) ^((k))+(j mod M)×Q _(ldpc)} mod(N _(ldpc) −K _(ldpc))  (2), where k=0, 1, 2, . . . D₁−1; i=0, 1, K_(ldpc)/M−1; and j=1, 2, . . . , M−1. Since j=1, 2, . . . , M−1, (j mod M) of Equation 2 may be regarded as j.

In the above equations, R_(i,j) ^((k)) is an index of a row where k^(th) 1 is located in the j^(th) column in the i^(th) column group, N_(ldpc) is a length of an LDPC codeword, K_(ldpc) is a length of information word bits, D_(i) is a degree of columns belonging to the i^(th) column group, M is the number of columns belonging to a single column group, and Q_(ldpc) is a size by which each column in the column group is cyclic-shifted.

As a result, referring to these equations, when only R_(i,0) ^((k)) is known, the index R_(i,j) ^((k)) of the row where the k^(th) 1 is located in the j^(th) column in the i^(th) column group can be known. Therefore, when the index value of the row where the k^(th) 1 is located in the 0^(th) column of each column group is stored, a position of column and row where 1 is located in the parity check matrix 200 having the configuration of FIG. 2 (that is, in the information word submatrix 210 of the parity check matrix 200) can be known.

According to the above-described rules, all of the columns belonging to the i^(th) column group have the same degree D_(i). Accordingly, the LDPC codeword which stores information on the parity check matrix according to the above-described rules may be briefly expressed as follows.

For example, when N_(ldpc) is 30, K_(ldpc) is 15, and Q_(ldpc) is 3, position information of the row where 1 is located in the 0^(th) column of the three column groups may be expressed by a sequence of Equations 3 and may be referred to as “weight-1 position sequence”. R _(1,0) ⁽¹⁾=1,R _(1,0) ⁽²⁾=2,R _(1,0) ⁽³⁾=8,R _(1,0) ⁽⁴⁾=10, R _(2,0) ⁽¹⁾=0,R _(2,0) ⁽²⁾=9,R _(2,0) ⁽³⁾=13, R _(3,0) ⁽¹⁾=0,R _(3,0) ⁽²⁾=14.  (3), where R_(i,j) ^((k)) is an index of a row where k^(th) 1 is located in the j^(th) column in the i^(th) column group.

The weight-1 position sequence like Equation 3 which expresses an index of a row where 1 is located in the 0^(th) column of each column group may be briefly expressed as in Table 3 presented below:

TABLE 3   1 2 8 10 0 9 13 0 14

Table 3 shows positions of elements having value 1 in the parity check matrix, and the i^(th) weight-1 position sequence is expressed by indexes of rows where 1 is located in the 0^(th) column belonging to the i^(th) column group.

The information word submatrix 210 of the parity check matrix according to an exemplary embodiment may be defined as in Tables 4 to 21 presented below, based on the above descriptions.

Specifically, Tables 4 to 21 show indexes of rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210. That is, the information word submatrix 210 is formed of a plurality of column groups each including M number of columns, and positions of 1 in the 0^(th) column of each of the plurality of column groups may be defined by Tables 4 to 21.

Herein, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group mean “addresses of parity bit accumulators”. The “addresses of parity bit accumulators” have the same meaning as defined in the DVB-C2/S2/T2 standards or the ATSC 3.0 standards which are currently being established, and thus, a detailed explanation thereof is omitted.

For example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 5/15, and M is 360, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are as shown in Table 4 presented below:

TABLE 4 Index of row where 1 is located in the i 0th column of the ith column group 0 245 449 491 980 1064 1194 1277 1671 2026 3186 4399 4900 5283 5413 5558 6570 7492 7768 7837 7984 8306 8483 8685 9357 9642 10045 10179 10261 10338 10412 1 1318 1584 1682 1860 1954 2000 2062 3387 3441 3879 3931 4240 4302 4446 4603 5117 5588 5675 5793 5955 6097 6221 6449 6616 7218 7394 9535 9896 10009 10763 2 105 472 785 911 1168 1450 2550 2851 3277 3624 4128 4460 4572 4669 4783 5102 5133 5199 5905 6647 7028 7086 7703 8121 8217 9149 9304 9476 9736 9884 3 1217 5338 5737 8334 4 855 994 2979 9443 5 7506 7811 9212 9982 6 848 3313 3380 3990 7 2095 4113 4620 9946 8 1488 2396 6130 7483 9 1002 2241 7067 10418 10 2008 3199 7215 7502 11 1161 7705 8194 8534 12 2316 4803 8649 9359 13 125 1880 3177 14 1141 8033 9072

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 7/15, and M is 360, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are as shown in Table 5 or 6 presented below:

TABLE 5 Index of row where 1 is located in the i 0th column of the ith column group 0 432 655 893 942 1285 1427 1738 2199 2441 2565 2932 3201 4144 4419 4678 4963 5423 5922 6433 6564 6656 7478 7514 7892 1 220 453 590 826 1116 1425 1488 1901 3119 3182 3568 3800 3953 4071 4782 5038 5555 6836 6871 7131 7609 7850 8317 8443 2 300 454 497 930 1757 2145 2314 2372 2467 2819 3191 3256 3699 3984 4538 4965 5461 5742 5912 6135 6649 7636 8078 8455 3 24 65 565 609 990 1319 1394 1465 1918 1976 2463 2987 3330 3677 4195 4240 4947 5372 6453 6950 7066 8412 8500 8599 4 1373 4663 5324 7777 5 189 3930 5766 6877 6 3 2961 4207 5747 7 1108 4768 6743 7106 8 1282 2274 2750 6204 9 2279 2587 2737 6344 10 2889 3164 7275 8040 11 133 2734 5081 8386 12 437 3203 7121 13 4280 7128 8490 14 619 4563 6206 15 2799 6814 6991 16 244 4212 5925 17 1719 7657 8554 18 53 1895 6685 19 584 5420 6856 20 2958 5834 8103

TABLE 6 Index of row where 1 is located in the i 0th column of the ith column group 0 553 742 9011327 1544 2179 2519 3131 3280 3603 3789 37924253 5340 5934 5962 6004 6698 7793 8001 8058 8126 8276 8559 1 503 590 598 1185 1266 1336 1806 2473 3021 3356 3490 3680 3936 4501 4659 5891 6132 6340 6602 7447 8007 8045 80598249 2 795 831 9471330 1502 2041 2328 2513 2814 2829 4048 4802 6044 6109 6461 6777 6800 7099 7126 8095 8428 8519 8556 8610 3 601 787 8991757 2259 2518 2783 2816 2823 2949 3396 43304494 4684 4700 4837 4881 4975 5130 5464 65546912 7094 8297 4 4229 5628 7917 7992 5 1506 3374 4174 5547 6 4275 5650 8208 8533 7 1504 1747 3433 6345 8 3659 6955 7575 7852 9 607 3002 4913 6453 10 3533 6850 7895 8048 11 4094 6366 8314 12 2206 4513 5411 13 32 3882 5149 14 389 3121 4626 15 1308 4419 6520 16 2092 2373 6849 17 1815 3679 7152 18 3582 3979 6948 19 1049 2135 3754 20 2276 4442 6591

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 9/15, and M is 360, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are as shown in Table 7 or 8 presented below:

TABLE 7 Index of row where 1 is located in the i 0th column of the ith column group 0 350 462 1291 1383 1821 2235 2493 3328 3353 3772 3872 3923 4259 4426 4542 4972 5347 6217 6246 6332 6386 1 177 859 1214 1253 1398 1482 1737 2014 2161 2331 3108 3297 3438 4388 4430 4456 4522 4783 5273 6037 6395 2 347 501 658 966 1622 1659 1934 2117 2527 3168 3231 3379 3427 3739 4218 4497 4894 5000 5167 5728 5975 3 319 398 599 1143 1796 3198 3521 3886 4139 4453 4556 4636 4688 4753 4986 5199 5224 5496 5698 5724 6123 4 162 257 304 524 945 1695 1855 2527 2780 2902 2958 3439 3484 4224 4769 4928 5156 5303 5971 6358 6477 5 807 1695 2941 4276 6 2652 2857 4660 6358 7 329 2100 2412 3632 8 1151 1231 3872 4869 9 1561 3565 5138 5303 10 407 794 1455 11 3438 5683 5749 12 1504 1985 3563 13 440 5021 6321 14 194 3645 5923 15 1217 1462 6422 16 1212 4715 5973 17 4098 5100 5642 18 5512 5857 6226 19 2583 5506 5933 20 784 1801 4890 21 4734 4779 4875 22 938 5081 5377 23 127 4125 4704 24 1244 2178 3352 25 3659 6350 6465 26 1686 3464 4336

TABLE 8 Index of row where 1 is located in the i 0th column of the ith column group 0 212 255 540 967 1033 1517 1538 3124 3408 3800 4373 4864 4905 5163 5177 6186 1 275 660 1351 2211 28763063 3433 4088 4273 4544 4618 4632 5548 6101 6111 6136 2 279 335 494865 1662 1681 3414 3775 4252 45955272 5471 5796 5907 5986 6008 3 345 352 3094 3188 42974338 4490 4865 5303 6477 4 222 681 1218 3169 3850 4878 4954 5666 6001 6237 5 172 512 1536 1559 21792227 3334 4049 6464 6 716 934 1694 2890 3276 3608 4332 4468 5945 7 1133 1593 1825 2571 3017 4251 5221 5639 5845 8 1076 1222 6465 9 159 5064 6078 10 374 4073 5357 11 2833 5526 5845 12 1594 3639 5419 13 1028 1392 4239 14 115 622 2175 15 300 1748 6245 16 2724 3276 5349 17 1433 6117 6448 18 485 663 4955 19 711 1132 4315 20 177 3266 4339 21 1171 4841 4982 22 33 1584 3692 23 2820 3485 4249 24 1716 2428 3125 25 250 2275 6338 26 108 1719 4961

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 11/15, and M is 360, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are as shown in Table 9 or 10 presented below:

TABLE 9 Index of row where 1 is located in the i 0th column of the ith column group 0 108 297 703 742 1345 1443 1495 1628 1812 2341 2559 2669 2810 2877 3442 3690 3755 3904 4264 1 180 211 477 788 824 1090 1272 1578 1685 1948 2050 2195 2233 2546 2757 2946 3147 3299 3544 2 627 741 1135 1157 1226 1333 1378 1427 1454 1696 1757 1772 2099 2208 2592 3354 3580 4066 4242 3 9 795 959 989 1006 1032 1135 1209 1382 1484 1703 1855 1985 2043 2629 2845 3136 3450 3742 4 230 413 801 829 1108 1170 1291 1759 1793 1827 1976 2000 2423 2466 2917 3010 3600 3782 4143 5 56 142 236 381 1050 1141 1372 1627 1985 2247 2340 3023 3434 3519 3957 4013 4142 4164 4279 6 298 1211 2548 3643 7 73 1070 1614 1748 8 1439 2141 3614 9 284 1564 2629 10 607 660 855 11 1195 2037 2753 12 49 1198 2562 13 296 1145 3540 14 1516 2315 2382 15 154 722 4016 16 759 2375 3825 17 162 194 1749 18 2335 2422 2632 19 6 1172 2583 20 726 1325 1428 21 985 2708 2769 22 255 2801 3181 23 2979 3720 4090 24 208 1428 4094 25 199 3743 3757 26 1229 2059 4282 27 458 1100 1387 28 1199 2481 3284 29 1161 1467 4060 30 959 3014 4144 31 2665 3960 4125 32 2809 3834 4318

TABLE 10 Index of row where 1 is located in the i 0th column of the ith column group 0 49 719 784 794 968 2382 2685 2873 2974 2995 3540 4179 1 272 281 374 1279 2034 2067 2112 3429 3613 3815 3838 4216 2 206 714 820 1800 1925 2147 2168 2769 2806 3253 3415 4311 3 62 159 166 605 1496 1711 2652 3016 3347 3517 3654 4113 4 363 733 1118 2062 2613 2736 3143 3427 3664 4100 4157 4314 5 57 142 436 983 1364 2105 2113 3074 3639 3835 4164 4242 6 870 921 950 1212 1861 2128 2707 2993 3730 3968 3983 4227 7 185 2684 3263 8 2035 2123 2913 9 883 2221 3521 10 1344 1773 4132 11 438 3178 3650 12 543 756 1639 13 1057 2337 2898 14 171 3298 3929 15 1626 2960 3503 16 484 3050 3323 17 2283 2336 4189 18 2732 4132 4318 19 225 2335 3497 20 600 2246 2658 21 1240 2790 3020 22 301 1097 3539 23 1222 1267 2594 24 1364 2004 3603 25 1142 1185 2147 26 564 1505 2086 27 697 991 2908 28 1467 2073 3462 29 2574 2818 3637 30 748 2577 2772 31 1151 1419 4129 32 164 1238 3401

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 13/15, and M is 360, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are as shown in Table 11 or 12 presented below:

TABLE 11 Index of row where 1 is located in the 0th column of the ith i column group 0 37 144 161 199 220 496 510 589 731 808 834 965 1249 1264 1311 1377 1460 1520 1598 1707 1958 2055 2099 2154 1 20 27 165 462 546 583 742 796 1095 1110 1129 1145 1169 1190 1254 1363 1383 1463 1718 1835 1870 1879 2108 2128 2 288 362 463 505 638 691 745 861 1006 1083 1124 1175 1247 1275 1337 1353 1378 1506 1588 1632 1720 1868 1980 2135 3 405 464 478 511 566 574 641 766 785 802 836 996 1128 1239 1247 1449 1491 1537 1616 1643 1668 1950 1975 2149 4 86 192 245 357 363 374 700 713 852 903 992 1174 1245 1277 1342 1369 1381 1417 1463 1712 1900 1962 2053 2118 5 101 327 378 550 6 186 723 1318 1550 7 118 277 504 1835 8 199 407 1776 1965 9 387 1253 1328 1975 10 62 144 1163 2017 11 100 475 572 2136 12 431 865 1568 2055 13 283 640 981 1172 14 220 1038 1903 2147 15 483 1318 1358 2118 16 92 961 1709 1810 17 112 403 1485 2042 18 431 1110 1130 1365 19 587 1005 1206 1588 20 704 1113 1943 21 375 1487 2100 22 1507 1950 2110 23 962 1613 2038 24 554 1295 1501 25 488 784 1446 26 871 1935 1964 27 54 1475 1504 28 1579 1617 2074 29 1856 1967 2131 30 330 1582 2107 31 40 1056 1809 32 1310 1353 1410 33 232 554 1939 34 168 641 1099 35 333 437 1556 36 153 622 745 37 719 931 1188 38 237 638 1607

TABLE 12 Index of row where 1 is located in the 0th column of the ith i column group 0 71 334 645 779 786 1124 1131 1267 1379 1554 1766 1798 1939 1 6 183 364 506 512 922 972 981 1039 1121 1537 1840 2111 2 6 71 153 204 253 268 781 799 873 1118 1194 1661 2036 3 6 247 353 581 921 940 1108 1146 1208 1268 1511 1527 1671 4 6 37 466 548 747 1142 1203 1271 1512 1516 1837 1904 2125 5 6 171 863 953 1025 1244 1378 1396 1723 1783 1816 1914 2121 6 1268 1360 1647 1769 7 6 458 1231 1414 8 183 535 1244 1277 9 107 360 498 1456 10 6 2007 2059 2120 11 1480 1523 1670 1927 12 139 573 711 1790 13 6 1541 1889 2023 14 6 374 957 1174 15 287 423 872 1285 16 6 1809 1918 17 65 818 1396 18 590 766 2107 19 192 814 1843 20 775 1163 1256 21 42 735 1415 22 334 1008 2055 23 109 596 1785 24 406 534 1852 25 684 719 1543 26 401 465 1040 27 112 392 621 28 82 897 1950 29 887 1962 2125 30 793 1088 2159 31 723 919 1139 32 610 839 1302 33 218 1080 1816 34 627 1646 1749 35 496 1165 1741 36 916 1055 1662 37 182 722 945 38 5 595 1674

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 6/15, and M is 360, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are as shown in Table 13 presented below:

TABLE 13 Index of row where 1 is located in the 0th column of the ith i column group 0 1606 3402 4961 6751 7132 11516 12300 12482 12592 13342 13764 14123 21576 23946 24533 25376 25667 26836 31799 34173 35462 36153 36740 37085 37152 37468 37658 1 4621 5007 6910 8732 9757 11508 13099 15513 16335 18052 19512 21319 23663 25628 27208 31333 32219 33003 33239 33447 36200 36473 36938 37201 37283 37495 38642 2 16 1094 2020 3080 4194 5098 5631 6877 7889 8237 9804 10067 11017 11366 13136 13354 15379 18934 20199 24522 26172 28666 30386 32714 36390 37015 37162 3 700 897 1708 6017 6490 7372 7825 9546 10398 16605 18561 18745 21625 22137 23693 24340 24966 25015 26995 28586 28895 29687 33938 34520 34858 37056 38297 4 159 2010 2573 3617 4452 4958 5556 5832 6481 8227 9924 10836 14954 15594 16623 18065 19249 22394 22677 23408 23731 24076 24776 27007 28222 30343 38371 5 3118 3545 4768 4992 5227 6732 8170 9397 10522 11508 15536 20218 21921 28599 29445 29758 29968 31014 32027 33685 34378 35867 36323 36728 36870 38335 38623 6 1264 4254 6936 9165 9486 9950 10861 11653 13697 13961 15164 15665 18444 19470 20313 21189 24371 26431 26999 28086 28251 29261 31981 34015 35850 36129 37186 7 111 1307 1628 2041 2524 5358 7988 8191 10322 11905 12919 14127 15515 15711 17061 19024 21195 22902 23727 24401 24608 25111 25228 27338 35398 37794 38196 8 961 3035 7174 7948 13355 13607 14971 18189 18339 18665 18875 19142 20615 21136 21309 21758 23366 24745 25849 25982 27583 30006 31118 32106 36469 36583 37920 9 2990 3549 4273 4808 5707 6021 6509 7456 8240 10044 12262 12660 13085 14750 15680 16049 21587 23997 25803 28343 28693 34393 34860 35490 36021 37737 38296 10 955 4323 5145 6885 8123 9730 11840 12216 19194 20313 23056 24248 24830 25268 26617 26801 28557 29753 30745 31450 31973 32839 33025 33296 35710 37366 37509 11 264 605 4181 4483 5156 7238 8863 10939 11251 12964 16254 17511 20017 22395 22818 23261 23422 24064 26329 27723 28186 30434 31956 33971 34372 36764 38123 12 520 2562 2794 3528 3860 4402 5676 6963 8655 9018 9783 11933 16336 17193 17320 19035 20606 23579 23769 24123 24966 27866 32457 34011 34499 36620 37526 13 10106 10637 10906 34242 14 1856 15100 19378 21848 15 943 11191 27806 29411 16 4575 6359 13629 19383 17 4476 4953 18782 24313 18 5441 6381 21840 35943 19 9638 9763 12546 30120 20 9587 10626 11047 25700 21 4088 15298 28768 35047 22 2332 6363 8782 28863 23 4625 4933 28298 30289 24 3541 4918 18257 31746 25 1221 25233 26757 34892 26 8150 16677 27934 30021 27 8500 25016 33043 38070 28 7374 10207 16189 35811 29 611 18480 20064 38261 30 25416 27352 36089 38469 31 1667 17614 25839 32776 32 4118 12481 21912 37945 33 5573 13222 23619 31271 34 18271 26251 27182 30587 35 14690 26430 26799 34355 36 13688 16040 20716 34558 37 2740 14957 23436 32540 38 3491 14365 14681 36858 39 4796 6238 25203 27854 40 1731 12816 17344 26025 41 19182 21662 23742 27872 42 6502 13641 17509 34713 43 12246 12372 16746 27452 44 1589 21528 30621 34003 45 12328 20515 30651 31432 46 3415 22656 23427 36395 47 632 5209 25958 31085 48 619 3690 19648 37778 49 9528 13581 26965 36447 50 2147 26249 26968 28776 51 15698 18209 30683 52 1132 19888 34111 53 4608 25513 38874 54 475 1729 34100 55 7348 32277 38587 56 182 16473 33082 57 3865 9678 21265 58 4447 20151 27618 59 6335 14371 38711 60 704 9695 28858 61 4856 9757 30546 62 1993 19361 30732 63 756 28000 29138 64 3821 24076 31813 65 4611 12326 32291 66 7628 21515 34995 67 1246 13294 30068 68 6466 33233 35865 69 14484 23274 38150 70 21269 36411 37450 71 23129 26195 37653

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 7/15, and M is 360, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are as shown in Table 14 presented below:

TABLE 14 Index of row where 1 is located in the 0th column of the ith i column group 0 7 15 26 69 1439 3712 5756 5792 5911 8456 10579 19462 19782 21709 23214 25142 26040 30206 30475 31211 31427 32105 32989 33082 33502 34116 34241 34288 34292 34318 34373 34390 34465 1 83 1159 2271 6500 6807 7823 10344 10700 13367 14162 14242 14352 15015 17301 18952 20811 24974 25795 27868 28081 33077 33204 33262 33350 33516 33677 33680 33930 34090 34250 34290 34377 34398 2 25 2281 2995 3321 6006 7482 8428 11489 11601 14011 17409 26210 29945 30675 31101 31355 31421 31543 31697 32056 32216 33282 33453 33487 33696 34044 34107 34213 34247 34261 34276 34467 34495 3 0 43 87 2530 4485 4595 9951 11212 12270 12344 15566 21335 24699 26580 28518 28564 28812 29821 30418 31467 31871 32513 32597 33187 33402 33706 33838 33932 33977 34084 34283 34440 34473 4 81 3344 5540 7711 13308 15400 15885 18265 18632 22209 23657 27736 29158 29701 29845 30409 30654 30855 31420 31604 32519 32901 33267 33444 33525 33712 33878 34031 34172 34432 34496 34502 34541 5 42 50 66 2501 4706 6715 6970 8637 9999 14555 22776 26479 27442 27984 28534 29587 31309 31783 31907 31927 31934 32313 32369 32830 33364 33434 33553 33654 33725 33889 33962 34467 34482 6 6534 7122 8723 13137 13183 15818 18307 19324 20017 26389 29326 31464 32678 33668 34217 7 50 113 2119 5038 5581 6397 6550 10987 22308 25141 25943 29299 30186 33240 33399 8 7262 8787 9246 10032 10505 13090 14587 14790 16374 19946 21129 25726 31033 33660 33675 9 5004 5087 5291 7949 9477 11845 12698 14585 15239 17486 18100 18259 21409 21789 24280 10 28 82 3939 5007 6682 10312 12485 14384 21570 25512 26612 26854 30371 31114 32689 11 437 3055 9100 9517 12369 19030 19950 21328 24196 24236 25928 28458 30013 32181 33560 12 18 3590 4832 7053 8919 21149 24256 26543 27266 30747 31839 32671 33089 33571 34296 13 2678 4569 4667 6551 7639 10057 24276 24563 25818 26592 27879 28028 29444 29873 34017 14 72 77 2874 9092 10041 13669 20676 20778 25566 28470 28888 30338 31772 32143 33939 15 296 2196 7309 11901 14025 15733 16768 23587 25489 30936 31533 33749 34331 34431 34507 16 6 8144 12490 13275 14140 18706 20251 20644 21441 21938 23703 34190 34444 34463 34495 17 5108 14499 15734 19222 24695 25667 28359 28432 30411 30720 34161 34386 34465 34511 34522 18 61 89 3042 5524 12128 22505 22700 22919 24454 30526 33437 34114 34188 34490 34502 19 11 83 4668 4856 6361 11633 15342 16393 16958 26613 29136 30917 32559 34346 34504 20 3185 9728 25062 21 1643 5531 21573 22 2285 6088 24083 23 78 14678 19119 24 49 13705 33535 25 21192 32280 32781 26 10753 21469 22084 27 10082 11950 13889 28 7861 25107 29167 29 14051 34171 34430 30 706 894 8316 31 29693 30445 32281 32 10202 30964 34448 33 15815 32453 34463 34 4102 21608 24740 35 4472 29399 31435 36 1162 7118 23226 37 4791 33548 34096 38 1084 34099 34418 39 1765 20745 33714 40 1302 21300 33655 41 33 8736 16646 42 53 18671 19089 43 21 572 2028 44 3339 11506 16745 45 285 6111 12643 46 27 10336 11586 47 21046 32728 34538 48 22215 24195 34026 49 19975 26938 29374 80 16473 26777 34212 51 20 29260 32784 52 35 31645 32837 53 26132 34410 34495 54 12446 20649 26851 55 6796 10992 31061 56 0 46 8420 57 10 636 22885 58 7183 16342 18305 59 1 5604 28258 60 6071 18675 34489 61 16786 25023 33323 62 3573 5081 10925 63 5067 31761 34415 64 3735 33534 34522 65 85 32829 34518 66 6555 23368 34559 67 22083 29335 29390 68 6738 21110 34316 69 120 4192 11123 70 3313 4144 20824 71 27783 28550 31034 72 6597 8164 34427 73 18009 23474 32460 74 94 6342 12656 75 17 31962 34535 76 15091 24955 28545 77 15 3213 28298 78 26562 30236 34537 79 16832 20334 24628 80 4841 20669 26509 81 18055 23700 34534 82 23576 31496 34492 83 10699 13826 34440

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 8/15, and M is 360, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are as shown in Table 15 presented below:

TABLE 15 Index of row where 1 is located in the 0th column of the ith i column group 0 2768 3039 4059 5856 6245 7013 8157 9341 9802 10470 11521 12083 16610 18361 20321 24601 27420 28206 29788 1 2739 8244 8891 9157 12624 12973 15534 16622 16919 18402 18780 19854 20220 20543 22306 25540 27478 27678 28053 2 1727 2268 6246 7815 9010 9556 10134 10472 11389 14599 15719 16204 17342 17666 18850 22058 25579 25860 29207 3 28 1346 3721 5565 7019 9240 12355 13109 14800 16040 16839 17369 17631 19357 19473 19891 20381 23911 29683 4 869 2450 4386 5316 6160 7107 10362 11132 11271 13149 16397 16532 17113 19894 22043 22784 27383 28615 28804 5 508 4292 5831 8559 10044 10412 11283 14810 15888 17243 17538 19903 20528 22090 22652 27235 27384 28208 28485 6 389 2248 5840 6043 7000 9054 11075 11760 12217 12565 13587 15403 19422 19528 21493 25142 27777 28566 28702 7 1015 2002 5764 6777 9346 9629 11039 11153 12690 13068 13990 16841 17702 20021 24106 26300 29332 30081 30196 8 1480 3084 3467 4401 4798 5187 7851 11368 12323 14325 14546 16360 17158 18010 21333 25612 26556 26906 27005 9 6925 8876 12392 14529 15253 15437 19226 19950 20321 23021 23651 24393 24653 26668 27205 28269 28529 29041 29292 10 2547 3404 3538 4666 5126 5468 7695 8799 14732 15072 15881 17410 18971 19609 19717 22150 24941 27908 29018 11 888 1581 2311 5511 7218 9107 10454 12252 13662 15714 15894 17025 18671 24304 25316 25556 28489 28977 29212 12 1047 1494 1718 4645 5030 6811 7868 8146 10611 15767 17682 18391 22614 23021 23763 25478 26491 29088 29757 13 59 1781 1900 3814 4121 8044 8906 9175 11156 14841 15789 16033 16755 17292 18550 19310 22505 29567 29850 14 1952 3057 4399 9476 10171 10769 11335 11569 15002 19501 20621 22642 23452 24360 25109 25290 25828 28503 29122 15 2895 3070 3437 4764 4905 6670 9244 11845 13352 13573 13975 14600 15871 17996 19672 20079 20579 25327 27958 16 612 1528 2004 4244 4599 4926 5843 7684 10122 10443 12267 14368 18413 19058 22985 24257 26202 26596 27899 17 1361 2195 4146 6708 7158 7538 9138 9998 14862 15359 16076 18925 21401 21573 22503 24146 24247 27778 29312 18 5229 6235 7134 7655 9139 13527 15408 16058 16705 18320 19909 20901 22238 22437 23654 25131 27550 28247 29903 19 697 2035 4887 5275 6909 9166 11805 15338 16381 18403 20425 20688 21547 24590 25171 26726 28848 29224 29412 20 5379 17329 22659 23062 21 11814 14759 22329 22936 22 2423 2811 10296 12727 23 8460 15260 16769 17290 24 14191 14608 29536 30187 25 7103 10069 20111 22850 26 4285 15413 26448 29069 27 548 2137 9189 10928 28 4581 707 23382 23949 29 3942 17248 19486 27922 30 8668 10230 16922 26678 31 6158 9980 13788 28198 32 12422 16076 24206 29887 33 8778 10649 18747 22111 34 21029 22677 27150 28980 35 7918 15423 27672 27803 36 5927 18086 23525 37 3397 15058 30224 38 24016 25880 26268 39 1096 4775 7912 40 3259 17301 20802 41 129 8396 15132 42 17825 28119 28676 43 2343 8382 28840 44 3907 18374 20939 45 1132 1290 8786 46 1481 4710 28846 47 2185 3705 26834 48 5496 15681 21854 49 12697 13407 22178 50 12788 21227 22894 51 629 2854 6232 52 2289 18227 27458 53 7593 21935 23001 54 3836 7081 12282 55 7925 18440 23135 56 497 6342 9717 57 11199 22046 30067 58 12572 28045 28990 59 1240 2023 10933 60 19566 20629 25186 61 6442 13303 28813 62 4765 10572 16180 63 552 19301 24286 64 6782 18480 21383 65 11267 12288 15758 66 771 5652 15531 67 16131 20047 25649 68 13227 23035 24450 69 4839 13467 27488 70 2852 4677 22993 71 2504 28116 29524 72 12518 17374 24267 73 1222 11859 27922 74 9660 17286 18261 75 232 11296 29978 76 9750 11165 16295 77 4894 9505 23622 78 10861 11980 14110 79 2128 15883 22836 80 6274 17243 21989 81 10866 13202 22517 82 11159 16111 21608 83 3719 18787 22100 84 1756 2020 23901 85 20913 29473 30103 86 2729 15091 26976 87 4410 8217 12963 88 5395 24564 28235 89 3859 17909 23051 90 5733 26005 29797 91 1935 3492 29773 92 11903 21380 29914 93 6091 10469 29997 94 2895 8930 15594 95 1827 10028 20070

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 9/15, and M is 360, the indexes of the rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are as shown in Table 16 presented below:

TABLE 16 Index of row where 1 is located in the 0th column of the ith i column group 0 113 1557 3316 5680 6241 10407 13404 13947 14040 14353 15522 15698 16079 17363 19374 19543 20530 22833 24339 1 271 1361 6236 7006 7307 7333 12768 15441 15568 17923 18341 20321 21502 22023 23938 25351 25590 25876 25910 2 73 605 872 4008 6279 7653 10346 10799 12482 12935 13604 15909 16526 19782 20506 22804 23629 24859 25600 3 1445 1690 4304 4851 8919 9176 9252 13783 16076 16675 17274 18806 18882 20819 21958 22451 23869 23999 24177 4 1290 2337 5661 6371 8996 10102 10941 11360 12242 14918 16808 20571 23374 24046 25045 25060 25662 25783 25913 5 28 42 1926 3421 3503 8558 9453 10168 15820 17473 19571 19685 22790 23336 23367 23890 24061 25657 25680 6 0 1709 4041 4932 5968 7123 8430 9564 10596 11026 14761 19484 20762 20858 23803 24016 24795 25853 25863 7 29 1625 6500 6609 16831 18517 18568 18738 19387 20159 20544 21603 21941 24137 24269 24416 24803 25154 25395 8 55 66 871 3700 11426 13221 15001 16367 17601 18380 22796 23488 23938 25476 25635 25678 25807 25857 25872 9 1 19 5958 8548 8860 11489 16845 18450 18469 19496 20190 23173 25262 25566 25668 25679 25858 25888 25915 10 7520 7690 8855 9183 14654 16695 17121 17854 18083 18428 19633 20470 20736 21720 22335 23273 25083 25293 25403 11 48 58 410 1299 3786 10668 18523 18963 20864 22106 22308 23033 23107 23128 23990 24286 24409 24595 25802 12 12 51 3894 6539 8276 10885 11644 12777 13427 14039 15954 17078 19053 20537 22863 24521 25087 25463 25838 13 3509 8748 9581 11509 15884 16230 17583 19264 20900 21001 21310 22547 22756 22959 24768 24814 25594 25626 25880 14 21 29 69 1448 2386 4601 6626 6667 10242 13141 13852 14137 18640 19951 22449 23454 24431 25512 25814 15 18 53 7890 9934 10063 16728 19040 19809 20825 21522 21800 23582 24556 25031 25547 25562 25733 25789 25906 16 4096 4582 5766 5894 6517 10027 12182 13247 15207 17041 18958 20133 20505 22228 24332 24613 25689 25855 25883 17 0 25 819 5539 7076 7536 7695 9532 13668 15051 17683 19665 20253 21996 24136 24890 25758 25784 25807 18 34 40 44 4215 6076 7427 7965 8777 11017 15593 19542 22202 22973 23397 23423 24418 24873 25107 25644 19 1595 6216 22850 25439 20 1562 15172 19517 22362 21 7508 12879 24324 24496 22 6298 15839 16757 18721 23 11173 15175 19966 21195 24 59 13505 16941 23793 25 2267 4830 12023 20587 26 8827 9278 13072 16664 27 14419 17463 23398 25348 28 6112 16534 20423 22698 29 493 8914 21103 24799 30 6896 12761 13206 25873 31 2 1380 12322 21701 32 11600 21306 25753 25790 33 8421 13076 14271 15401 34 9630 14112 19017 20955 35 212 13932 21781 25824 36 5961 9110 16654 19636 37 58 5434 9936 12770 38 6575 11433 19798 39 2731 7338 20926 40 14253 18463 25404 41 21791 24805 25869 42 2 11646 15850 43 6075 8586 23819 44 18435 22093 24852 45 2103 2368 11704 46 10925 17402 18232 47 9062 25061 25674 48 18497 20853 23404 49 18606 19364 19551 50 7 1022 25543 51 6744 15481 25868 52 9081 17305 25164 53 8 23701 25883 54 9680 19955 22848 55 56 4564 19121 56 5595 15086 25892 57 3174 17127 23183 58 19397 19817 20275 59 12561 24571 25825 60 7111 9889 25865 61 19104 20189 21851 62 549 9686 25548 63 6586 20325 25906 64 3224 20710 21637 65 641 15215 25754 66 13484 23729 25818 67 2043 7493 24246 68 16860 25230 25768 69 22047 24200 24902 70 9391 18040 19499 71 7855 24336 25069 72 23834 25570 25852 73 1977 8800 25756 74 6671 21772 25859 75 3279 6710 24444 76 24099 25117 25820 77 5553 12306 25915 78 48 11107 23907 79 10832 11974 25773 80 2223 17905 25484 81 16782 17135 20446 82 475 2861 3457 83 16218 22449 24362 84 11716 22200 25897 85 8315 15009 22633 86 13 20480 25852 87 12352 18658 25687 88 3681 14794 23703 89 30 24531 25846 90 4103 22077 24107 91 23837 25622 25812 92 3627 13387 25839 93 908 5367 19388 94 0 6894 25795 95 20322 23546 25181 96 8178 25260 25437 97 2449 13244 22565 98 31 18928 22741 99 1312 5134 14838 100 6085 13937 24220 101 66 14633 25670 102 47 22512 25472 103 8867 24704 25279 104 6742 21623 22745 105 147 9948 24178 106 8522 24261 24307 107 19202 22406 24609

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 10/15, and M is 360, the indexes of rows where 1 is located in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are defined as shown in Table 17 or 18 below:

TABLE 17 Index of row where 1 is located in the 0th column of the ith i column group 0 979 1423 4166 4609 6341 8258 10334 10548 14098 14514 17051 17333 17653 17830 17990 1 2559 4025 6344 6510 9167 9728 11312 14856 17104 17721 18600 18791 19079 19697 19840 2 3243 6894 7950 10539 12042 13233 13938 14752 16449 16727 17025 18297 18796 19400 21577 3 3272 3574 6341 6722 9191 10807 10957 12531 14036 15580 16651 17007 17309 19415 19845 4 155 4598 10201 10975 11086 11296 12713 15364 15978 16395 17542 18164 18451 18612 20617 5 1128 1999 3926 4069 5558 6085 6337 8386 10693 12450 15438 16223 16370 17308 18634 6 2408 2929 3630 4357 5852 7329 8536 8695 10603 11003 14304 14937 15767 18402 21502 7 199 3066 6446 6849 8973 9536 10452 12857 13675 15913 16717 17654 19802 20115 21579 8 312 870 2095 2586 5517 6196 6757 7311 7368 13046 15384 18576 20349 21424 21587 9 985 1591 3248 3509 3706 3847 6174 6276 7864 9033 13618 15675 16446 18355 18843 10 975 3774 4083 5825 6166 7218 7633 9657 10103 13052 14240 17320 18126 19544 20208 11 1795 2005 2544 3418 6148 8051 9066 9725 10676 10752 11512 15171 17523 20481 21059 12 167 315 1824 2325 2640 2868 6070 6597 7016 8109 9815 11608 16142 17912 19625 13 1298 1896 3039 4303 4690 8787 12241 13600 14478 15492 16602 17115 17913 19466 20597 14 568 3695 6045 6624 8131 8404 8590 9059 9246 11570 14336 18657 18941 19218 21506 15 228 1889 1957 2299 3011 5074 7044 7596 7689 9534 10244 10697 11691 17902 21410 16 1330 1579 1739 2234 3701 3865 5713 6677 7263 11172 12143 12765 17121 20011 21436 17 303 1668 2501 4925 5778 5985 9635 10140 10820 11779 11849 12058 15650 20426 20527 18 698 2484 3071 3219 4054 4125 5663 5939 6928 7086 8054 12173 16280 17945 19302 19 232 1619 3040 4901 7438 8135 9117 9233 10131 13321 17347 17436 18193 18586 19929 20 12 3721 6254 6609 7880 8139 10437 12262 13928 14065 14149 15032 15694 16254 18883 21 482 915 1548 1637 6687 9338 10163 11768 11970 15524 15695 17386 18787 19210 19340 22 1291 2500 4109 4511 5099 5194 10014 13165 13256 13972 15409 16113 16214 18584 20998 23 1761 4778 7444 7740 8129 8341 8931 9136 9207 10003 10678 13959 17673 18194 20990 24 3060 3522 5361 5692 6833 8342 8792 11023 11211 11548 11914 13987 15442 15541 19707 25 1322 2348 2970 5632 6349 7577 8782 9113 9267 9376 12042 12943 16680 16970 21321 26 6785 11960 21455 27 1223 15672 19550 28 5976 11335 20385 29 2818 9387 15317 30 2763 3554 18102 31 5230 11489 18997 32 5809 15779 20674 33 2620 17838 18533 34 3025 9342 9931 35 3728 5337 12142 36 2520 6666 9164 37 12892 15307 20912 38 10736 12393 16539 39 1075 2407 12853 40 4921 5411 18206 41 5955 15647 16838 42 6384 10336 19266 43 429 10421 17266 44 4880 10431 12208 45 2910 11895 12442 46 7366 18362 18772 47 4341 7903 14994 48 4564 6714 7378 49 4639 8652 18871 50 15787 18048 20246 51 3241 11079 13640 52 1559 2936 15881 53 2737 6349 10881 54 10394 16107 17073 55 8207 9043 12874 56 7805 16058 17905 57 11189 15767 17764 58 5823 12923 14316 59 11080 20390 20924 60 568 8263 17411 61 1845 3557 6562 62 2890 10936 14756 63 9031 14220 21517 64 3529 12955 15902 65 413 6750 8735 66 6784 12092 16421 67 12019 13794 15308 68 12588 15378 17676 69 8067 14589 19304 70 1244 5877 6085 71 15897 19349 19993 72 1426 2394 12264 73 3456 8931 12075 74 13342 15273 20351 75 9138 13352 20798 76 7031 7626 14081 77 4280 4507 15617 78 4170 10569 14335 79 3839 7514 16578 80 4688 12815 18782 81 4861 7858 9435 82 605 5445 12912 83 2280 4734 7311 84 6668 8128 12638 85 3733 10621 19534 86 13933 18316 19341 87 1786 3037 21566 88 2202 13239 16432 89 4882 5808 9300 90 4580 8484 16754 91 14630 17502 18269 92 6889 11119 12447 93 8162 9078 16330 94 6538 17851 18100 95 17763 19793 20816 96 2183 11907 17567 97 6640 14428 15175 98 877 12035 14081 99 1336 6468 12328 100 5948 9146 12003 101 3782 5699 12445 102 1770 7946 8244 103 7384 12639 14989 104 1469 11586 20959 105 7943 10450 15907 106 5005 8153 10035 107 17750 18826 21513 108 4725 8041 10112 109 3837 16266 17376 110 11340 17361 17512 111 1269 4611 4774 112 2322 10813 16157 113 16752 16843 18959 114 70 4325 18753 115 3165 8153 15384 116 160 8045 16823 117 14112 16724 16792 118 4291 7667 18176 119 5943 19879 20721

TABLE 18 Index of row where 1 is located in the 0th column of the ith i column group 0 316 1271 3692 9495 12147 12849 14928 16671 16938 17864 19108 20502 21097 21115 1 2341 2559 2643 2816 2865 5137 5331 7000 7523 8023 10439 10797 13208 15041 2 5556 6858 7677 10162 10207 11349 12321 12398 14787 15743 15859 15952 19313 20879 3 349 573 910 2702 3654 6214 9246 9353 10638 11772 14447 14953 16620 19888 4 204 1390 2887 3835 6230 6533 7443 7876 9299 10291 10896 13960 18287 20086 5 541 2429 2838 7144 8523 8637 10490 10585 11074 12074 15762 16812 17900 18548 6 733 1659 3838 5323 5805 7882 9429 10682 13697 16909 18846 19587 19592 20904 7 1134 2136 4631 4653 4718 5197 10410 11666 14996 15305 16048 17417 18960 20303 8 734 1001 1283 4959 10016 10176 10973 11578 12051 15550 15915 19022 19430 20121 9 745 4057 5855 9885 10594 10989 13156 13219 13351 13631 13685 14577 17713 20386 10 968 1446 2130 2502 3092 3787 5323 8104 8418 9998 11681 13972 17747 17929 11 3020 3857 5275 5786 6319 8608 11943 14062 17144 17752 18001 18453 19311 21414 12 709 747 1038 2181 5320 8292 10584 10859 13964 15009 15277 16953 20675 21509 13 1663 3247 5003 5760 7186 7360 10346 14211 14717 14792 15155 16128 17355 17970 14 516 578 1914 6147 9419 11148 11434 13289 13325 13332 19106 19257 20962 21556 15 5009 5632 6531 9430 9886 10621 11765 13969 16178 16413 18110 18249 20616 20759 16 457 2686 3318 4608 5620 5858 6480 7430 9602 12691 14664 18777 20152 20848 17 33 2877 5334 6851 7907 8654 10688 15401 16123 17942 17969 18747 18931 20224 18 87 897 7636 8663 11425 12288 12672 14199 16435 17615 17950 18953 19667 20281 19 1042 1832 2545 2719 2947 3672 3700 6249 6398 6833 11114 14283 17694 20477 20 326 488 2662 2880 3009 5357 6587 8882 11604 14374 18781 19051 19057 20508 21 854 1294 2436 2852 4903 6466 7761 9072 9564 10321 13638 15658 16946 19119 22 194 899 1711 2408 2786 5391 7108 8079 8716 11453 17303 19484 20989 21389 23 1631 3121 3994 5005 7810 8850 10315 10589 13407 17162 18624 18758 19311 20301 24 736 2424 4792 5600 6370 10061 16053 16775 18600 25 1254 8163 8876 9157 12141 14587 16545 17175 18191 26 388 6641 8974 10607 10716 14477 16825 17191 18400 27 5578 6082 6824 7360 7745 8655 11402 11665 12428 28 3603 8729 13463 14698 15210 19112 19550 20727 21052 29 48 1732 3805 5158 15442 16909 19854 21071 21579 30 11707 14014 21531 31 1542 4133 4925 32 10083 13505 21198 33 14300 15765 16752 34 778 1237 11215 35 1325 3199 14534 36 2007 14510 20599 37 1996 5881 16429 38 5111 15018 15980 39 4989 10681 12810 40 3763 10715 16515 41 2259 10080 15642 42 9032 11319 21305 43 3915 15213 20884 44 11150 15022 20201 45 1147 6749 19625 46 12139 12939 18870 47 3840 4634 10244 48 1018 10231 17720 49 2708 13056 13393 50 5781 11588 18888 51 1345 2036 5252 52 5908 8143 15141 53 1804 13693 18640 54 10433 13965 16950 55 9568 10122 15945 56 547 6722 14015 57 321 12844 14095 58 2632 10513 14936 59 6369 11995 20321 60 9920 19136 21529 61 1990 2726 10183 62 5763 12118 15467 63 503 10006 19564 64 9839 11942 19472 65 11205 13552 15389 66 8841 13797 19697 67 124 6053 18224 68 6477 14406 21146 69 1224 8027 16011 70 3046 4422 17717 71 739 12308 17760 72 4014 4130 7835 73 2266 5652 11981 74 2711 7970 18317 75 2196 15229 17217 76 8636 13302 16764 77 5612 15010 16657 78 615 1249 4639 79 3821 12073 18506 80 1066 16522 21536 81 11307 18363 19740 82 3240 8560 10391 83 3124 11424 20779 84 1604 8861 17394 85 2083 7400 8093 86 3218 7454 9155 87 9855 15998 20533 88 316 2850 20652 89 5583 9768 10333 90 7147 7713 18339 91 12607 17428 21418 92 14216 16954 18164 93 8477 15970 18488 94 1632 8032 9751 95 4573 9080 13507 96 11747 12441 13876 97 1183 15605 16675 98 4408 10264 17109 99 5495 7882 12150 100 1010 3763 5065 101 9828 18054 21599 102 6342 7353 15358 103 6362 9462 19999 104 7184 13693 17622 105 4343 4654 10995 106 7099 8466 18520 107 11505 14395 15138 108 6779 16691 18726 109 7146 12644 20196 110 5865 16728 19634 111 4657 8714 21246 112 4580 5279 18750 113 3767 6620 18905 114 9209 13093 17575 115 12486 15875 19791 116 8046 14636 17491 117 2120 4643 13206 118 6186 9675 12601 119 784 5770 21585

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 11/15, and M is 360, the indexes of rows where 1 is located in the 0^(th) column of the 1^(th) column group of the information word submatrix 210 are defined as shown in Table 19 below.

TABLE 19 Index of row where 1 is located in the 0th column of the ith i column group 0 696 989 1238 3091 3116 3738 4269 6406 7033 8048 9157 10254 12033 16456 16912 1 444 1488 6541 8626 10735 12447 13111 13706 14135 15195 15947 16453 16916 17137 17268 2 401 460 992 1145 1576 1678 2238 2320 4280 6770 10027 12486 15363 16714 17157 3 1161 3108 3727 4508 5092 5348 5582 7727 11793 12515 12917 13362 14247 16717 17205 4 542 1190 6883 7911 8349 8835 10489 11631 14195 15009 15454 15482 16632 17040 17063 5 17 487 776 880 5077 6172 9771 11446 12798 16016 16109 16171 17087 17132 17226 6 1337 3275 3462 4229 9246 10180 10845 10866 12250 13633 14482 16024 16812 17186 17241 7 15 980 2305 3674 5971 8224 11499 11752 11770 12897 14082 14836 15311 16391 17209 8 0 3926 5869 8696 9351 9391 11371 14052 14172 14636 14974 16619 16961 17033 17237 9 3033 5317 6501 8579 10698 12168 12966 14019 15392 15806 15991 16493 16690 17062 17090 10 981 1205 4400 6410 11003 13319 13405 14695 15846 16297 16492 16563 16616 16862 16953 11 1725 4276 8869 9588 14062 14486 15474 15548 16300 16432 17042 17050 17060 17175 17273 12 1807 5921 9960 10011 14305 14490 14872 15852 16054 16061 16306 16799 16833 17136 17262 13 2826 4752 6017 6540 7016 8201 14245 14419 14716 15983 16569 16652 17171 17179 17247 14 1662 2516 3345 5229 8086 9686 11456 12210 14595 15808 16011 16421 16825 17112 17195 15 2890 4821 5987 7226 8823 9869 12468 14694 15352 15805 16075 16462 17102 17251 17263 16 3751 3890 4382 5720 10281 10411 11350 12721 13121 14127 14980 15202 15335 16735 17123 17 26 30 2805 5457 6630 7188 7477 7556 11065 16608 16859 16909 16943 17030 17103 18 40 4524 5043 5566 9645 10204 10282 11696 13080 14837 15607 16274 17034 17225 17266 19 904 3157 6284 7151 7984 11712 12887 13767 15547 16099 16753 16829 17044 17250 17259 20 7 311 4876 8334 9249 11267 14072 14559 15003 15235 15686 16331 17177 17238 17253 21 4410 8066 8596 9631 10369 11249 12610 15769 16791 16960 17018 17037 17062 17165 17204 22 24 8261 9691 10138 11607 12782 12786 13424 13933 15262 15795 16476 17084 17193 17220 23 88 11622 14735 15890 24 304 2026 2638 6018 25 1163 4268 11620 17232 26 9701 11785 14463 17260 27 4118 10952 12224 17006 28 3647 10823 11521 12060 29 1717 3753 9199 11642 30 2187 14280 17220 31 14787 16903 17061 32 381 3534 4294 33 3149 6947 8323 34 12562 16724 16881 35 7289 9997 15306 36 5615 13152 17260 37 5666 16926 17027 38 4190 7798 16831 39 4778 10629 17180 40 10001 13884 15453 41 6 2237 8203 42 7831 15144 15160 43 9186 17204 17243 44 9435 17168 17237 45 42 5701 17159 46 7812 14259 15715 47 39 4513 6658 48 38 9368 11273 49 1119 4785 17182 50 5620 16521 16729 51 165685 17242 52 210 3452 12383 53 466 14462 16250 54 10548 12633 13962 55 1452 6005 16453 56 22 4120 13684 57 5195 11563 16522 58 5518 16705 17201 59 12233 14552 15471 60 6067 13440 17248 61 8660 8967 17061 62 8673 12176 15051 63 5959 15767 16541 64 3244 12109 12414 65 31 15913 16323 66 3270 15686 16653 67 24 7346 14675 68 12 1531 8740 69 6228 7565 16667 70 16936 17122 17162 71 4868 8451 13183 72 3714 4451 16919 73 11313 13801 17132 74 17070 17191 17242 75 1911 11201 17186 76 14 17190 17254 77 11760 16008 16832 78 14543 17033 17278 79 16129 16765 17155 80 6891 15561 17007 81 12741 14744 17116 82 8992 16661 17277 83 1861 11130 16742 84 4822 13331 16192 85 13281 14027 14989 86 38 14887 17141 87 10698 13452 15674 88 4 2539 16877 89 857 17170 17249 90 11449 11906 12867 91 285 14118 16831 92 15191 17214 17242 93 39 728 16915 94 2469 12969 15579 95 16644 17151 17164 96 2592 8280 10448 97 9236 12431 17173 98 9064 16892 17233 99 4526 16146 17038 100 31 2116 16083 101 15837 16951 17031 102 5362 8382 16618 103 6137 13199 17221 104 2841 15068 17068 105 24 3620 17003 106 9880 15718 16764 107 1784 10240 17209 108 2731 10293 10846 109 3121 8723 16598 110 8563 15662 17088 111 13 1167 14676 112 29 13850 15963 113 3654 7553 8114 114 23 4362 14865 115 4434 14741 16688 116 8362 13901 17244 117 13687 16736 17232 118 46 4229 13394 119 13169 16383 16972 120 16031 16681 16952 121 3384 9894 12580 122 9841 14414 16165 123 5013 17099 17115 124 2130 8941 17266 125 6907 15428 17241 126 16 1860 17235 127 2151 16014 16643 128 14954 15958 17222 129 3969 8419 15116 130 31 15593 16984 131 11514 16605 17255

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 12/15, and M is 360, the indexes of rows where 1 is located in the 0^(th) column of the 1^(th) column group of the information word submatrix 210 are defined as shown in Table 20 below.

TABLE 20 Index of row where 1 is located in the 0th column of the ith i column group 0 584 1472 1621 1867 3338 3568 3723 4185 5126 5889 7737 8632 8940 9725 1 221 445 590 3779 3835 6939 7743 8280 8448 8491 9367 10042 11242 12917 2 4662 4837 4900 5029 6449 6687 6751 8684 9936 11681 11811 11886 12089 12909 3 2418 3018 3647 4210 4473 7447 7502 9490 10067 11092 11139 11256 12201 12383 4 2591 2947 3349 3406 4417 4519 5176 6672 8498 8863 9201 11294 11376 12184 5 27 101 197 290 871 1727 3911 5411 6676 8701 9350 10310 10798 12439 6 1765 1897 2923 3584 3901 4048 6963 7054 7132 9165 10184 10824 11278 12669 7 2183 3740 4808 5217 5660 6375 6787 8219 8466 9037 10353 10583 11118 12762 8 73 1594 2146 2715 3501 3572 3639 3725 6959 7187 8406 10120 10507 10691 9 240 732 1215 2185 2788 2830 3499 3881 4197 4991 6425 7061 9756 10491 10 831 1568 1828 3424 4319 4516 4639 6018 9702 10203 10417 11240 11518 12458 11 2024 2970 3048 3638 3576 4152 5284 5779 5926 9426 9945 10873 11787 11837 12 1049 1218 1651 2328 3493 4363 5750 6483 7613 8782 9738 9803 11744 11937 13 1193 2060 2289 2964 3478 4592 4756 6709 7162 8231 8326 11140 11908 12243 14 978 2120 2439 3338 3850 4589 6567 8745 9656 9708 10161 10542 10711 12639 15 2403 2938 3117 3247 3711 5593 5844 5932 7801 10152 10226 11498 12162 12941 16 1781 2229 2276 2533 3582 3951 5279 5774 7930 9824 10920 11038 12340 12440 17 289 384 1980 2230 3464 3873 5958 8656 8942 9006 10175 11425 11745 12530 18 155 354 1090 1330 2002 2236 3559 3705 4922 5958 6576 8564 9972 12760 19 303 876 2059 2142 5244 5330 6644 7576 8614 9598 10410 10718 11033 12957 20 3449 3617 4408 4602 4727 6182 8835 8928 9372 9644 10237 10747 11655 12747 21 811 2565 2820 8677 8974 9632 11069 11548 11839 12107 12411 12695 12812 12890 22 972 4123 4943 6385 6449 7339 7477 8379 9177 9359 10074 11709 12552 12831 23 842 973 1541 2262 2905 5276 6758 7099 7894 8128 8325 8663 8875 10050 24 474 791 968 3902 4924 4965 5085 5908 6109 6329 7931 9038 9401 10568 25 1397 4461 4658 5911 6037 7127 7318 8678 8924 9000 9473 9602 10446 12692 26 1334 7571 12881 27 1393 1447 7972 28 633 1257 10597 29 4843 5102 11056 30 3294 8015 10513 31 1108 10374 10546 32 5353 7824 10111 33 3398 7674 8569 34 7719 9478 10503 35 2997 9418 9581 36 5777 6519 11229 37 1966 5214 9899 38 6 4088 5827 39 836 9248 9612 40 483 7229 7548 41 7865 8289 9804 42 2915 11098 11900 43 6180 7096 9481 44 1431 6786 8924 45 748 6757 8625 46 3312 4475 7204 47 1852 8958 11020 48 1915 2903 4006 49 6776 10886 12531 50 2594 9998 12742 51 159 2002 12079 52 853 3281 3762 53 5201 5798 6413 54 3882 6062 12047 55 4133 6775 9657 56 228 6874 11183 57 7433 10728 10864 58 7735 8073 12734 59 2844 4621 11779 60 3909 7103 12804 61 6002 9704 11060 62 5864 6856 7681 63 3652 5869 7605 64 2546 2657 4461 65 2423 4203 9111 66 244 1855 4691 67 1106 2178 6371 68 391 1617 10126 69 250 9259 10603 70 3435 4614 6924 71 1742 8045 9529 72 7667 8875 11451 73 4023 6108 6911 74 8621 10184 11650 75 6726 10861 12348 76 3228 6302 7388 77 1 1137 5358 78 381 2424 8537 79 3256 7508 10044 80 1980 2219 4569 81 2468 5699 10319 82 2803 3314 12808 83 8578 9642 11533 84 829 4585 7923 85 59 329 5575 86 1067 5709 6867 87 1175 4744 12219 88 109 2518 6756 89 2105 10626 11153 90 5192 10696 10749 91 6260 7641 8233 92 2998 3094 11214 93 3398 6466 11494 94 6574 10448 12160 95 2734 10755 12780 96 1028 7958 10825 97 8545 8602 10793 98 392 3398 11417 99 6639 9291 12571 100 1067 7919 8934 101 1064 2848 12753 102 6076 8656 12690 103 5504 6193 10171 104 1951 7156 7356 105 4389 4780 7889 106 526 4804 9141 107 1238 3648 10464 108 2587 5624 12557 109 5560 5903 11963 110 1134 2570 3297 111 10041 11583 12157 112 1263 9585 12912 113 3744 7898 10646 114 45 9074 10315 115 1051 6188 10038 116 2242 8394 12712 117 3598 9025 12651 118 2295 3540 5610 119 1914 4378 12423 120 1766 3635 12759 121 5177 9586 11143 122 943 3590 11649 123 4864 6905 10454 124 5852 6042 10421 125 6095 8285 12349 126 2070 7171 8563 127 718 12234 12716 128 512 10667 11353 129 3629 6485 7040 130 2880 8865 11466 131 4490 10220 11796 132 5440 8819 9103 133 5262 7543 12411 134 516 7779 10940 135 2515 5843 9202 136 4684 5994 10586 137 573 2270 3324 138 7870 8317 10322 139 6856 7638 12909 140 1583 7669 10781 141 8141 9085 12555 142 3903 5485 9992 143 4467 11998 12904

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 13/15, and M is 360, the indexes of rows where 1 exists in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are defined as shown in Table 21 below:

TABLE 21 Index of row where 1 is located in the i 0th column of the ith column group 0 142 2307 2598 2650 4028 4434 5781 5881 6016 6323 6681 6698 8125 1 2932 4928 5248 5256 5983 6773 6828 7789 8426 8494 8534 8539 8583 2 899 3295 3833 5399 6820 7400 7753 7890 8109 8451 8529 8564 8602 3 21 3060 4720 5429 5636 5927 6966 8110 8170 8247 8355 8365 8616 4 20 1745 2838 3799 4380 4418 4646 5059 7343 8161 8302 8456 8631 5 9 6274 6725 6792 7195 7333 8027 8186 8209 8273 8442 8548 8632 6 494 1365 2405 3799 5188 5291 7644 7926 8139 8458 8504 8594 8625 7 192 574 1179 4387 4695 5089 5831 7673 7789 8298 8301 8612 8632 8 11 20 1406 6111 6176 6256 6708 6834 7828 8232 8457 8495 8602 9 6 2654 3554 4483 4966 5866 6795 8069 8249 8301 8497 8509 8623 10 21 1144 2355 3124 6773 6805 6887 7742 7994 8358 8374 8580 8611 11 335 4473 4883 5528 6096 7543 7586 7921 8197 8319 8394 8489 8636 12 2919 4331 4419 4735 6366 6393 6844 7193 8165 8205 8544 8586 8617 13 12 19 742 930 3009 4330 6213 6224 7292 7430 7792 7922 8137 14 710 1439 1588 2434 3516 5239 6248 6827 8230 8448 8515 8581 8619 15 200 1075 1868 5581 7349 7642 7698 8037 8201 8210 8320 8391 8526 16 3 2501 4252 5256 5292 5567 6136 6321 6430 6486 7571 8521 8636 17 3062 4599 5885 6529 6616 7314 7319 7567 8024 8153 8302 8372 8598 18 105 381 1574 4351 5452 5603 5943 7467 7788 7933 8362 8513 8587 19 787 1857 3386 3659 6550 7131 7965 8015 8040 8312 8484 8525 8537 20 15 1118 4226 5197 5575 5761 6762 7038 8260 8338 8444 8512 8568 21 36 5216 5368 5616 6029 6591 8038 8067 8299 8351 8565 8578 8585 22 1 23 4300 4530 5426 5532 5817 6967 7124 7979 8022 8270 8437 23 629 2133 4828 5475 5875 5890 7194 8042 8345 8385 8518 8598 8612 24 11 1065 3782 4237 4993 7104 7863 7904 8104 8228 8321 8383 8565 25 2131 2274 3168 3215 3220 5597 6347 7812 8238 8354 8527 8557 8614 26 5600 6591 7491 7696 27 1766 8281 8626 28 1725 2280 5120 29 1650 3445 7652 30 4312 6911 8626 31 15 1013 5892 32 2263 2546 2979 33 1545 5873 7406 34 67 726 3697 35 2860 6443 8542 36 17 911 2820 37 1561 4580 6052 38 79 5269 7134 39 22 2410 2424 40 3501 5642 8627 41 808 6950 8571 42 4099 6389 7482 43 4023 5000 7833 44 5476 5765 7917 45 1008 3194 7207 46 20 495 5411 47 1703 8388 8635 48 6 4395 4921 49 200 2053 8206 50 1089 5126 5562 51 10 4193 7720 52 1967 2151 4608 53 22 738 3513 54 3385 5066 8152 55 440 1118 8537 56 3429 6058 7716 57 5213 7519 8382 58 5564 8365 8620 59 43 3219 8603 60 4 5409 5815 61 5 6376 7654 62 4091 5724 5953 63 5348 6754 8613 64 1634 6398 6632 65 72 2058 8605 66 3497 5811 7579 67 3846 6743 8559 68 15 5933 8629 69 2133 5859 7068 70 4151 4617 8566 71 2960 8270 8410 72 2059 3617 8210 73 544 1441 6895 74 4043 7482 8592 75 294 2180 8524 76 3058 8227 8373 77 364 5756 8617 78 5383 8555 8619 79 1704 2480 4181 80 7338 7929 7990 81 2615 3905 7981 82 4298 4548 8296 83 8262 8319 8630 84 892 1893 8028 85 5694 7237 8595 86 1487 5012 5810 87 4335 8593 8624 88 3509 4531 5273 89 10 22 830 90 4161 5208 6280 91 275 7063 8634 92 4 2725 3113 93 2279 7403 8174 94 1637 3328 3930 95 2810 4939 5624 96 3 1234 7687 97 2799 7740 8616 98 22 7701 8636 99 4302 7857 7993 100 7477 7794 8592 101 9 6111 8591 102 5 8606 8628 103 347 3497 4033 104 1747 2613 8636 105 1827 5600 7042 106 580 1822 6842 107 232 7134 7783 108 4629 5000 7231 109 951 2806 4947 110 571 3474 8577 111 2437 2496 7945 112 23 5873 8162 113 12 1168 7686 114 8315 8540 8596 115 1766 2506 4733 116 929 1516 3338 117 21 1216 6555 118 782 1452 8617 119 8 6083 6087 120 667 3240 4583 121 4030 4661 5790 122 559 7122 8553 123 3202 4388 4909 124 2533 3673 8594 125 1991 3954 6206 126 6835 7900 7980 127 189 5722 8573 128 2680 4928 4998 129 243 2579 7735 130 4281 8132 8566 131 7656 7671 8609 132 1116 2291 4166 133 21 388 8021 134 6 1123 8369 135 311 4918 8511 136 0 3248 6290 137 13 6762 7172 138 4209 5632 7563 139 49 127 8074 140 581 1735 4075 141 0 2235 5470 142 2178 5820 6179 143 16 3575 6054 144 1095 4564 6458 145 9 1581 5953 146 2537 6469 8552 147 14 3874 4844 148 0 3269 3551 149 2114 7372 7926 150 1875 2388 4057 151 3232 4042 6663 152 9 401 583 153 13 4100 6584 154 2299 4190 4410 155 21 3670 4979

According to an exemplary embodiment, even when the order of numbers in a sequence corresponding to the i^(th) column group of the parity check matrix 200 as shown in the above-described Tables 4 to 21 is changed, the changed parity check matrix is a parity check matrix used for the same code. Therefore, a case in which the order of numbers in the sequence corresponding to the i^(th) column group in Tables 4 to 21 is changed is covered by the inventive concept.

According to an exemplary embodiment, even when the arrangement order of sequences corresponding to each column group is changed in Tables 4 to 21, cycle characteristics on a graph of a code and algebraic characteristics such as degree distribution are not changed. Therefore, a case in which the arrangement order of the sequences shown in Tables 4 to 21 is changed is also covered by the inventive concept.

In addition, even when a multiple of Q_(ldpc) is equally added to all sequences corresponding to a certain column group in Tables 4 to 21, the cycle characteristics on the graph of the code or the algebraic characteristics such as degree distribution are not changed. Therefore, a result of equally adding a multiple of Q_(ldpc) to the sequences shown in Tables 4 to 21 is also covered by the inventive concept. However, it should be noted that, when the resulting value obtained by adding the multiple of Q_(ldpc) to a given sequence is greater than or equal to (N_(ldpc)−K_(ldpc)), a value obtained by applying a modulo operation for (N_(ldpc)−K_(ldpc)) to the resulting value should be applied instead.

Once positions of the rows where 1 exists in the 0^(th) column of the i^(th) column group of the information word submatrix 210 are defined as shown in Tables 4 to 21, positions of rows where 1 exists in another column of each column group may be defined since the positions of the rows where 1 exists in the 0^(th) column are cyclic-shifted by Q_(ldpc) in the next column.

For example, in the case of Table 4, in the 0^(th) column of the 0^(th) column group of the information word submatrix 210, 1 exists in the 245^(th) row, 449^(th) row, 491^(st) row, . . . .

In this case, since Q_(ldpc)=(N_(ldpc)−K_(ldpc))/M=(16200−5400)/360=30, the indexes of the rows where 1 is located in the 1^(st) column of the 0^(th) column group may be 275(=245+30), 479(=449+30), 521(=491+30), . . . , and the indexes of the rows where 1 is located in the 2^(nd) column of the 0^(th) column group may be 305(=275+30), 509(=479+30), 551(=521+30), . . . .

In the above-described method, the indexes of the rows where 1 is located in all rows of each column group may be defined.

The parity submatrix 220 of the parity check matrix 200 shown in FIG. 2 may be defined as follows:

The parity submatrix 220 includes N_(ldpc)−K_(ldpc) number of columns (that is, K_(ldpc) ^(th) column to (N_(lpdc)−1)^(th) column), and has a dual diagonal or staircase configuration. Accordingly, the degree of columns except the last column (that is, (N_(ldpc)−1)^(th) column) from among the columns included in the parity submatrix 220 is 2, and the degree of the last column is 1.

As a result, the information word submatrix 210 of the parity check matrix 200 may be defined by Tables 4 to 21, and the parity submatrix 220 of the parity check matrix 200 may have a dual diagonal configuration.

When the columns and rows of the parity check matrix 200 shown in FIG. 2 are permutated based on Equation 4 and Equation 5, the parity check matrix shown in FIG. 2 may be changed to a parity check matrix 300 shown in FIG. 3. Q _(ldpc) ·i+j⇒M·j+i(0≤i<M,0≤j<Q _(ldpc))  (4) K _(ldpc) +Q _(ldpc) ·k+l⇒K _(ldpc) +M·l+k(0≤k<M,0≤l<Q _(ldpc))  (5)

The method for permutating based on Equation 4 and Equation 5 will be explained below. Since row permutation and column permutation apply the same principle, the row permutation will be explained by the way of an example.

In the case of the row permutation, regarding the X^(th) row, i and j satisfying X=Q_(ldpc)×i+j are calculated and the X^(th) row is permutated by assigning the calculated i and j to M×j+i. For example, regarding the 7^(th) row, i and j satisfying 7=2×i+j are 3 and 1, respectively. Therefore, the 7^(th) row is permutated to the 13^(th) row (10×1+3=13).

When the row permutation and the column permutation are performed in the above-described method, the parity check matrix of FIG. 2 may be converted into the parity check matrix of FIG. 3.

Referring to FIG. 3, the parity check matrix 300 is divided into a plurality of partial blocks, and a quasi-cyclic matrix of M×M corresponds to each partial block.

Accordingly, the parity check matrix 300 having the configuration of FIG. 3 is formed of matrix units of M×M. That is, the submatrices of M×M are arranged in the plurality of partial blocks, constituting the parity check matrix 300.

Since the parity check matrix 300 is formed of the quasi-cyclic matrices of M×M, M number of columns may be referred to as a column block and M number of rows may be referred to as a row block. Accordingly, the parity check matrix 300 having the configuration of FIG. 3 is formed of N_(qc) _(_) _(column)=N_(ldpc)/M number of column blocks and N_(qc) _(_) _(row)=N_(parity)/M number of row blocks.

Hereinafter, the submatrix of M×M will be explained.

First, the (N_(qc) _(_) _(column)−1)^(th) column block of the 0^(th) row block has a form shown in Equation 6 presented below:

$\begin{matrix} {A = \begin{bmatrix} 0 & 0 & \ldots & 0 & 0 \\ 1 & 0 & \ldots & 0 & 0 \\ 0 & 1 & \ldots & 0 & 0 \\ M & M & M & M & M \\ 0 & 0 & \ldots & 1 & 0 \end{bmatrix}} & (6) \end{matrix}$

As described above, A 330 is an M×M matrix, values of the 0^(th) row and the (M−1)^(th) column are all “0”, and, regarding 0≤i≤(M−2), the (i+1)^(th) row of the i^(th) column is “1” and the other values are “0”.

Second, regarding 0≤i≤(N_(ldpc)−K_(ldpc))/M−1 in the parity submatrix 320, the i^(th) row block of the (K_(ldpc)/M+i)^(th) column block is configured by a unit matrix I_(M×M) 340. In addition, regarding 0≤i≤(N_(ldpc)−K_(ldpc))/M−2, the (i+1)^(th) row block of the (K_(ldpc)/M+i)^(th) column block is configured by a unit matrix I_(M×M) 340.

Third, a block 350 constituting the information word submatrix 310 may have a cyclic-shifted format of a cyclic matrix P, P^(a) ^(ij) , or an added format of the cyclic-shifted matrix P^(a) ^(ij) of the cyclic matrix P (or an overlapping format).

For example, a format in which the cyclic matrix P is cyclic-shifted to the right by 1 may be expressed by Equation 7 presented below:

$\begin{matrix} {P = \begin{bmatrix} 0 & 1 & 0 & \; & 0 \\ 0 & 0 & 1 & \Lambda & 0 \\ M & M & M & \; & M \\ 0 & 0 & 0 & \Lambda & 1 \\ 1 & 0 & 0 & \; & 0 \end{bmatrix}} & (7) \end{matrix}$

The cyclic matrix P is a square matrix having an M×M size and is a matrix in which a weight of each of M number of rows is 1 and a weight of each of M number of columns is 1. When a_(ij) is 0, the cyclic matrix P, that is, P⁰ indicates a unit matrix I_(M×M), and when a_(ij) is ∞, P^(∞) is a zero matrix.

A submatrix existing where the i^(th) row block and the j^(th) column block intersect in the parity check matrix 300 of FIG. 3 may be P^(a) ^(ij) . Accordingly, i and j indicate the number of row blocks and the number of column blocks in the partial blocks corresponding to the information word. Accordingly, in the parity check matrix 300, the total number of columns is N_(ldpc)=M×N_(qc) _(_) _(column), and the total number of rows is N_(parity)=M×N_(qc) _(_) _(row). That is, the parity check matrix 300 is formed of N_(qc) _(_) _(column) number of “column blocks” and N_(qc) _(_) _(row) number of “row blocks”.

Hereinafter, a method for performing LDPC encoding based on the parity check matrix 200 as shown in FIG. 2 will be explained. An LDPC encoding process when the parity check matrix 200 is defined as shown in Table 10 by way of an example will be explained for the convenience of explanation.

First, when information word bits having a length of K_(ldpc) are [i₀, i₁, i₂, . . . , i_(K) _(ldp) ₋₁], and parity bits having a length of N_(ldpc)−K_(ldpc) are [p₀, p₁, p₂, . . . p_(N) _(ldpc) _(−K) _(ldpc) ⁻¹], the LDPC encoding is performed by the following process.

Step 1) Parity bits are initialized as ‘0’. That is, p₀=p₁=p₂= . . . =p_(N) _(ldpc) _(−K) _(ldpc) ⁻¹=0.

Step 2) The 0^(th) information word bit i₀ is accumulated in a parity bit having the address of the parity bit defined in the first row (that is, the row of i=0) of Table 10 as the index of the parity bit. This may be expressed by Equation 8 presented below:

$\begin{matrix} {{P_{49} = {P_{49} \oplus i_{0}}}{P_{719} = {P_{719} \oplus i_{0}}}{P_{784} = {P_{784} \oplus i_{0}}}{P_{794} = {P_{794} \oplus i_{0}}}{P_{968} = {P_{968} \oplus i_{0}}}{P_{2382} = {P_{2382} \oplus i_{0}}}{P_{2685} = {P_{2685} \oplus i_{0}}}{P_{2873} = {P_{2873} \oplus i_{0}}}{P_{2974} = {P_{2974} \oplus i_{0}}}{P_{2995} = {P_{2995} \oplus i_{0}}}{P_{3540} = {P_{3540} \oplus i_{0}}}{P_{4179} = {P_{4179} \oplus i_{0}}}} & (8) \end{matrix}$

Herein, i₀ is a 0^(th) information word bit, p_(i) is an ith parity bit, and ⊕ is a binary operation. According to the binary operation, 1 ⊕1 equals 0, 1β0 equals 1, 0⊕1 equals 1, 0⊕0 equals 0.

Step 3) The other 359 information word bits i_(m) (m=1, 2, . . . , 359) are accumulated in the parity bit. The other information word bits may belong to the same column group as that of i₀. In this case, the address of the parity bit may be determined based on Equation 9 presented below: (x+(m mod 360)×Q _(ldpc))mod(N _(ldpc) −K _(ldpc))  (9)

Herein, x is an address of a parity bit accumulator corresponding to the information word bit i₀, and Q_(ldpc) is a size by which each column is cyclic-shifted in the information word submatrix, and may be 12 in the case of Table 10. In addition, since m=1, 2, . . . , 359, (m mod 360) in Equation 9 may be regarded as m.

As a result, information word bits i_(m) (m=1, 2, . . . , 359) are accumulated in the parity bits having the address of the parity bit calculated based on Equation 9 as the index. For example, an operation as shown in Equation 10 presented below may be performed for the information word bit i₁:

$\begin{matrix} {{P_{61} = {P_{61} \oplus i_{1}}}{P_{731} = {P_{731} \oplus i_{1}}}{P_{796} = {P_{796} \oplus i_{1}}}{P_{806} = {P_{806} \oplus i_{1}}}{P_{980} = {P_{980} \oplus i_{1}}}{P_{2394} = {P_{2394} \oplus i_{1}}}{P_{2697} = {P_{2697} \oplus i_{1}}}{P_{2885} = {P_{2885} \oplus i_{1}}}{P_{2986} = {P_{2986} \oplus i_{1}}}{P_{3007} = {P_{3007} \oplus i_{1}}}{P_{3552} = {P_{3552} \oplus i_{1}}}{P_{4191} = {P_{4191} \oplus i_{1}}}} & (10) \end{matrix}$

Herein, i₁ is a 1^(st) information word bit, p_(i) is an ith parity bit, and ⊕ is a binary operation. According to the binary operation, 1⊕1 equals 0, 1⊕0 equals 1, 0⊕1 equals 1, 0⊕0 equals 0.

Step 4) The 360^(th) information word bits i₃₆₀ is accumulated in a parity bit having the address of the parity bit defined in the 2^(nd) row (that is, the row of i=1) of Table 10 as the index of the parity bit.

Step 5) The other 359 information word bits belonging to the same group as that of the information word bit i₃₆₀ are accumulated in the parity bit. In this case, the address of the parity bit may be determined based on Equation 9. However, in this case, x is the address of the parity bit accumulator corresponding to the information word bit i₃₆₀.

Step 6) Steps 4 and 5 described above are repeated for all of the column groups of Table 10.

Step 7) As a result, a parity bit p_(i) is calculated based on Equation 11 presented below. In this case, i is initialized as 1. p _(i) =p _(i) ⊕p _(i−1) i=1,2, . . . ,N _(ldpc) −K _(ldpc)−1  (11)

In Equation 11, p₁ is an ith parity bit, N_(ldpc) is a length of an LDPC codeword, K_(ldpc), is a length of an information word of the LDPC codeword, and ⊕ is a binary operation.

As a result, the encoder 110 may calculate the parity bits according to the above-described method.

In another example, a parity check matrix according to an exemplary embodiment may have a configuration as shown in FIG. 4.

Referring to FIG. 4, the parity check matrix 400 may be formed of 5 matrices A, B, C, Z, and D. Hereinafter, the configuration of each matrix will be explained to explain the configuration of the parity check matrix 400.

First, M₁, M₂, Q₁, and Q₂, which are parameter values related to the parity check matrix 400 as shown in FIG. 4, may be defined as shown in Table 22 presented below according to the length and the code rate of the LDPC codeword.

TABLE 22 Sizes Rate Length M₁ M₂ Q₁ Q₂ 1/15 16200 2520 12600 7 35 64800 1080 59400 3 165 2/15 16200 3240 10800 9 30 64800 1800 54360 5 151 3/15 16200 1080 11880 3 33 64800 1800 50040 5 139 4/15 16200 1080 10800 3 30 64800 1800 45720 5 127 5/15 16200 720 10080 2 28 64800 1440 41760 4 116 6/15 16200 1080 8640 3 24 64800 1080 37800 3 105

The matrix A is formed of K number of columns and g number of rows, and the matrix C is formed of K+g number of columns and N−K−g number of rows. Herein, K is a length of information word bits, and N is a length of the LDPC codeword.

Indexes of rows where 1 is located in the 0^(th) column of the ith column group in the matrix A and the matrix C may be defined based on Tables 23 to 31 according to the length and the code rate of the LDPC codeword. In this case, an interval at which a pattern of a column is repeated in each of the matrix A and the matrix C, that is, the number of columns belonging to the same group, may be 360.

For example, when the length N of the LDPC codeword is 64800 and the code rate is 3/15, the indexes of rows where 1 is located in the 0^(th) column of the ith column group in the matrix A and the matrix C are defined as shown in Table 23 presented below:

TABLE 23 i Index of row where 1 is located in the 0th column of the ith column group 0 920 963 1307 2648 6529 17455 18883 19848 19909 24149 24249 38395 41589 48032 50313 1 297 736 744 5951 8438 9881 15522 16462 23036 25071 34915 41193 42975 43412 49612 2 10 223 879 4662 6400 8691 14561 16626 17408 22810 31795 32580 43639 45223 47511 3 629 842 1666 3150 7596 9465 12327 18649 19052 19279 29743 30197 40106 48371 51155 4 857 953 1116 8725 8726 10508 17112 21007 30649 32113 36962 39254 46636 49599 50099 5 700 894 1128 5527 6216 15123 21510 24584 29026 31416 37158 38460 42511 46932 51832 6 430 592 1521 3018 10430 18090 18092 18388 20017 34383 35006 38255 41700 42158 45211 7 91 1485 1733 11624 12969 17531 21324 23657 27148 27509 28753 35093 43352 48104 51648 8 18 34 117 6739 8679 11018 12163 16733 24113 25906 30605 32700 36465 40799 43359 9 481 1545 1644 4216 4606 6015 6609 14659 16966 18056 19137 26670 28001 30668 49061 10 174 1208 1387 10580 11507 13751 16344 22735 23559 26492 27672 33399 44787 44842 45992 11 1151 1185 1472 6727 10701 14755 15688 17441 21281 23692 23994 31366 35854 37301 43148 12 200 799 1583 3451 5880 7604 8194 13428 16109 18584 20463 22373 31977 47073 50087 13 346 843 1352 13409 17376 18233 19119 19382 20578 24183 32052 32912 43204 48539 49893 14 76 457 1169 13516 14520 14638 22391 25294 31067 31325 36711 44072 44854 49274 51624 15 759 798 1420 6661 12101 12573 13796 15510 18384 26649 30875 36856 38994 43634 49281 16 551 797 1000 3999 10040 11246 15793 23298 23822 38480 39209 45334 46603 46625 47633 17 441 875 1554 5336 25948 28842 30329 31503 39203 39673 46250 47021 48555 49229 51421 18 963 1470 1642 3180 3943 6513 9125 15641 17083 18876 28499 32764 42420 43922 45762 19 293 324 867 8803 10582 17926 19830 22497 24848 30034 34659 37721 41523 42534 47806 20 687 975 1356 2721 3002 3874 4119 12336 17119 21251 22482 22833 24681 26225 48514 21 549 951 1268 9144 11710 12623 18949 19362 22769 32603 34559 34683 36338 47140 51069 22 52 890 1669 3905 5670 14712 18314 22297 30328 33389 35447 35512 35516 40587 41918 23 656 1063 1694 3338 3793 4513 6009 7441 13393 20920 26501 27576 29623 31261 42093 24 425 1018 1086 9226 10024 17552 24714 24877 25853 28918 30945 31205 33103 42564 47214 25 32 1145 1438 4916 4945 14830 17505 19919 24118 28506 30173 31754 34230 48608 50291 26 559 1216 1272 2856 8703 9371 9708 16180 19127 24337 26390 36649 41105 42988 44096 27 362 658 1191 7769 8998 14068 15921 18471 18780 31995 32798 32864 37293 39468 44308 28 1136 1389 1785 8800 12541 14723 15210 15859 26569 30127 31357 32898 38760 50523 51715 29 44 80 1368 2010 2228 6614 6767 9275 25237 30208 39537 42041 49906 50701 51199 30 1522 1536 1765 3914 5350 10869 12278 12886 16379 22743 23987 26306 30966 33854 41356 31 212 648 709 3443 7007 7545 12484 13358 17008 20433 25862 31945 39207 39752 40313 32 789 1062 1431 12280 17415 18098 23729 37278 38454 38763 41039 44600 50700 51139 51696 33 825 1298 1391 4882 12738 17569 19177 19896 27401 37041 39181 39199 41832 43636 45775 34 992 1053 1485 3806 16929 18596 22017 23435 23932 30211 30390 34469 37213 46220 49646 35 771 850 1039 5180 7653 13547 17980 23365 25318 34374 36115 38753 42993 49696 51031 36 7383 14780 15959 18921 22579 28612 32038 36727 40851 41947 42707 50480 37 8733 9464 13148 13899 19396 22933 23039 25047 29938 33588 33796 48930 38 2493 12555 16706 23905 35400 36330 37065 38866 40305 43807 43917 50621 39 6437 11927 14542 16617 17317 17755 18832 24772 29273 31136 36925 46663 40 2191 3431 6288 6430 9908 13069 23014 24822 29818 39914 46010 47246

In another example, when the length N of the LDPC codeword is 16200 and the code rate is 4/15, the indexes of rows where 1 is located in the 0^(th) column of the ith column group in the matrix A and the matrix C are defined as shown in Table 24 presented below:

TABLE 24 Indexes of rows where 1 is located in the i 0th column of the ith column group 0 19 585 710 3241 3276 3648 6345 9224 9890 10841 1 181 494 894 2562 3201 4382 5130 5308 6493 10135 2 150 569 919 1427 2347 4475 7857 8904 9903 3 1005 1018 1025 2933 3280 3946 4049 4166 5209 4 420 554 778 6908 7959 8344 8462 10912 11099 5 231 506 859 4478 4957 7664 7731 7908 8980 6 179 537 979 3717 5092 6315 6883 9353 9935 7 147 205 830 3609 3720 4667 7441 10196 11809 8 60 1021 1061 1554 4918 5690 6184 7986 11296 9 145 719 768 2290 2919 7272 8561 9145 10233 10 388 590 852 1579 1698 1974 9747 10192 10255 11 231 343 485 1546 3155 4829 7710 10394 11336 12 4381 5398 5987 9123 10365 11018 11153 13 2381 5196 6613 6844 7357 8732 11082 14 1730 4599 5693 6318 7626 9231 10663

In another example, when the length N of the LDPC codeword is 64800 and the code rate is 4/15, the indexes of rows where 1 is located in the 0^(th) column of the ith column group in the matrix A and the matrix C are defined as shown in Table 25 presented below:

TABLE 25 Index of row where 1 is located in the i 0th column of the ith column group 0 276 1754 1780 3597 8549 15196 26305 27003 33883 37189 41042 41849 42356 1 730 873 927 9310 9867 17594 21969 25106 25922 31167 35434 37742 45866 2 925 1202 1564 2575 2831 2951 5193 13096 18363 20592 33786 34090 40900 3 973 1045 1071 8545 8980 11983 18649 21323 22789 22843 26821 36720 37856 4 402 1038 1689 2466 2893 13474 15710 24137 29709 30451 35568 35965 46436 5 263 271 395 5089 5645 15488 16314 28778 29729 34350 34533 39608 45371 6 387 1059 1306 1955 6990 20001 24606 28167 33802 35181 38481 38688 45140 7 53 851 1750 3493 11415 18882 20244 23411 28715 30722 36487 38019 45416 8 810 1044 1772 3906 5832 16793 17333 17910 23946 29650 34190 40673 45828 9 97 491 948 12156 13788 24970 33774 37539 39750 39820 41195 46464 46820 10 192 899 1283 3732 7310 13637 13810 19005 24227 26772 31273 37665 44005 11 424 531 1300 4860 8983 10137 16323 16888 17933 22458 26917 27835 37931 12 130 279 731 3024 6378 18838 19746 21007 22825 23109 28644 32048 34667 13 938 1041 1482 9589 10065 11535 17477 25816 27966 35022 35025 42536 14 170 454 1312 5326 6765 23408 24090 26072 33037 38088 42985 46413 15 220 804 843 2921 4841 7760 8303 11259 21058 21276 34346 37604 16 676 713 832 11937 12006 12309 16329 26438 34214 37471 38179 42420 17 714 931 1580 6837 9824 11257 15556 26730 32053 34461 35889 45821 18 28 1097 1340 8767 9406 17253 29558 32857 37856 38593 41781 47101 19 158 722 754 14489 23851 28160 30371 30579 34963 44216 46462 47463 20 833 1326 1332 7032 9566 11011 21424 26827 29789 31699 32876 37498 21 251 504 1075 4470 7736 11242 20397 32719 34453 36571 40344 46341 22 330 581 868 15168 20265 26354 33624 35134 38609 44965 45209 46909 23 729 1643 1732 3946 4912 9615 19699 30993 33658 38712 39424 46799 24 546 982 1274 9264 11017 11868 15674 16277 19204 28606 39063 43331 25 73 1160 1196 4334 12560 13583 14703 18270 18719 19327 38985 46779 26 1147 1625 1759 3767 5912 11599 18561 19330 29619 33671 43346 44098 27 104 1507 1586 9387 17890 23532 27008 27861 30966 33579 35541 39801 28 1700 1746 1793 4941 7814 13746 20375 27441 30262 30392 35385 42848 29 183 555 1029 3090 5412 8148 19662 23312 23933 28179 29962 35514 30 891 908 1127 2827 4077 4376 4570 26923 274556 33699 43431 46071 31 404 1110 1782 6003 14452 19247 26998 30137 31404 31624 46621 47366 32 886 1627 1704 8193 8980 9648 10928 16267 19774 35111 38545 44735 33 268 380 1214 4797 5168 9109 9288 17992 21309 33210 36210 41429 34 572 1121 1165 6944 7114 20978 23540 25863 26190 26365 41521 44690 35 18 185 496 5885 6165 20468 23895 24745 31226 33680 37665 38587 36 289 527 1118 11275 12015 18088 22805 24679 28262 30160 34892 43212 37 658 926 1589 7634 16231 22193 25320 26057 26512 27498 29472 34219 38 337 801 1525 2023 3512 16031 26911 32719 35620 39035 43779 44316 39 248 534 670 6217 11430 24090 26509 28712 33073 33912 38048 39813 40 82 1556 1575 7879 7892 14714 22404 22773 25531 34170 38203 38254 41 247 313 1224 3694 14304 24033 26394 28101 37455 37859 38997 41344 42 790 887 1418 2811 3288 9049 9704 13303 14262 38149 40109 40477 43 1310 1384 1471 3716 8250 25371 26329 26997 30138 40842 41041 44921 44 86 288 367 1860 8713 18211 22628 22811 28342 28463 40415 45845 45 719 1438 1741 8258 10797 29270 29404 32096 34433 34616 36030 45597 46 215 1182 1364 8146 9949 10498 18603 19304 19803 23685 43304 45121 47 1243 1496 1537 8484 8851 16589 17665 20152 24283 28993 34274 39795 48 6320 6785 15841 16309 20512 25804 27421 28941 43871 44647 49 2207 2713 4450 12217 16506 21188 23933 28789 38099 42392 50 14064 14307 14599 14866 17540 18881 21065 25823 30341 36963 51 14259 14396 17037 26769 29219 29319 31689 33013 35631 37319 52 7798 10495 12868 14298 17221 23344 31908 39809 41001 41965

In another example, when the length N of the LDPC codeword is 16200 and the code rate is 5/15, the indexes of rows where 1 is located in the 0^(th) column of the ith column group in the matrix A and the matrix C are defined as shown in Table 26 presented below:

TABLE 26 Index of rows where 1 is located in the i 0th column of the ith column group 0 69 244 706 5145 5994 6066 6763 6815 8509 1 257 541 618 3933 6188 7048 7484 8424 9104 2 69 500 536 1494 1669 7075 7553 8202 10305 3 11 189 340 2103 3199 6775 7471 7918 10530 4 333 400 434 1806 3264 5693 8534 9274 10344 5 111 129 260 3562 3676 3680 3809 5169 7308 8280 6 100 303 342 3133 3952 4226 4713 5053 5717 9931 7 83 87 374 828 2460 4943 6311 8657 9272 9571 8 114 166 325 2680 4698 7703 7886 8791 9978 10684 9 281 542 549 1671 3178 3955 7153 7432 9052 10219 10 202 271 608 3860 4173 4203 5169 6871 8113 9757 11 16 359 419 3333 4198 4737 6170 7987 9573 10095 12 235 244 584 4640 5007 5563 6029 6816 7678 9968 13 123 449 646 2460 3845 4161 6610 7245 7686 8651 14 136 231 468 835 2622 3292 5158 5294 6584 9926 15 3085 4683 8191 9027 9922 9928 10550 16 2462 3185 3976 4091 8089 8772 9342

In another example, when the length N of the LDPC codeword is 64800 and the code rate is 6/15, the indexes of rows where 1 is located in the 0^(th) column of the ith column group in the matrix A and the matrix C are defined as shown in Table 27 presented below:

TABLE 27 Indexes of rows where 1 is located in i the 0th column of the ith column group 0 221 1011 1218 4299 7143 8728 11072 15533 17356 33909 36833 1 360 1210 1375 2313 3493 16822 21373 23588 23656 26267 34098 2 544 1347 1433 2457 9186 10945 13583 14858 19195 34606 37441 3 37 596 715 4134 8091 12106 24307 24658 34108 40591 42883 4 235 398 1204 2075 6742 11670 13512 23231 24784 27915 34752 5 204 873 890 13550 16570 19774 34012 35249 37655 39885 42890 6 221 371 514 11984 14972 15690 28827 29069 30531 31018 43121 7 280 549 1435 1889 3310 10234 11575 15243 20748 30469 36005 8 223 666 1248 13304 14433 14732 18943 21248 23127 38529 39272 9 370 819 1065 9461 10319 25294 31958 33542 37458 39681 40039 10 585 870 1028 5087 5216 12228 16216 16381 16937 27132 27893 11 164 167 1210 7386 11151 20413 22713 23134 24188 36771 38992 12 298 511 809 4620 7347 8873 19602 24162 29198 34304 41145 13 105 830 1212 2415 14759 15440 16361 16748 22123 32684 42575 14 659 665 668 6458 22130 25972 30697 31074 32048 36078 37129 15 91 808 953 8015 8988 13492 13987 15979 28355 34509 39698 16 594 983 1265 3028 4029 9366 11069 11512 27066 40939 41639 17 506 740 1321 1484 10747 16376 17384 20285 31502 38925 42606 18 338 356 975 2022 3578 18689 18772 19826 22914 24733 27431 19 709 1264 1366 4617 8893 25226 27800 29080 30277 37781 39644 20 840 1179 1338 2973 3541 7043 12712 15005 17149 19910 36795 21 1009 1267 1380 4919 12679 22889 79638 30987 34637 36232 37284 22 466 913 1247 1646 3049 5924 9014 20539 34546 35029 36540 23 374 697 984 1654 5870 10883 11684 20294 28888 31612 34031 24 117 240 635 5093 8673 11323 12456 14145 21397 39619 42559 25 122 1265 1427 13528 14282 15241 16852 17227 34723 36836 39791 26 595 1180 1310 6952 17916 24725 24971 27243 29555 32138 35987 27 140 470 1017 13222 13253 18462 20806 21117 28673 31598 37235 28 7 710 1072 8014 10804 13303 14292 16690 26676 36443 41966 29 48 189 759 12438 14523 16388 23178 27315 28656 29111 29694 30 285 387 410 4294 4467 5949 25386 27898 34880 41169 42614 31 474 545 1320 10506 13186 18126 27110 31498 35353 36193 37322 32 1075 1130 1424 11390 13312 14161 16927 25071 25844 34287 38151 33 161 396 427 5944 17281 22201 25218 30143 35566 38261 42513 34 233 247 694 1446 3180 3507 9069 20764 21940 33422 39358 35 271 508 1013 6271 21760 21858 24887 29808 31099 35475 39924 36 8 674 1329 3135 5110 14460 28108 28388 31043 31137 31863 37 1035 1222 1409 8287 16083 24450 24888 29356 30329 37834 39684 38 391 1090 1128 1866 4095 10643 13121 14499 20056 22195 30593 39 55 161 1402 6289 6837 8791 17937 21425 26602 30461 37241 40 110 377 1228 6875 13253 17032 19008 23274 32285 33452 41630 41 360 638 1355 5933 12593 13533 23377 23881 24586 26040 41663 42 535 1240 1333 3354 10860 16032 32573 34908 34957 39255 40759 43 526 936 1321 7992 10260 18527 28248 29356 32636 34666 35552 44 336 785 875 7530 13062 13075 18925 27963 28703 33688 36502 45 36 591 1062 1518 3821 7048 11197 17781 19408 22731 24783 46 214 1145 1223 1546 9475 11170 16061 21273 38688 40051 42479 47 1136 1226 1423 20227 22573 24951 26462 29586 34915 42441 43048 48 26 276 1425 6048 7224 7917 8747 27559 28515 35002 37649 49 127 294 437 4029 8585 9647 11904 24115 28514 36893 39722 50 748 1093 1403 9536 19305 20468 31049 38667 40502 40720 41949 51 96 638 743 9806 12101 17751 22732 24937 32007 32594 38504 52 649 904 1079 2770 3337 9158 20125 24619 32921 33698 35173 53 401 518 984 7372 12438 12582 18704 35874 39420 39503 39790 54 10 451 1077 8078 16320 17409 25807 28814 30613 41261 42955 55 405 592 1178 15936 18418 19585 21966 24219 30637 34536 37838 56 50 584 851 9720 11919 22544 22545 25851 35567 41587 41876 57 911 1113 1176 1806 10058 10809 14220 19044 20748 29424 36671 58 441 550 1135 1956 11254 18699 30249 33099 34587 35243 39952 59 510 1016 1281 8621 13467 13780 15170 16289 20925 26426 34479 60 4969 5223 17117 21950 22144 24043 27151 39809 61 11452 13622 18918 19670 23995 32647 37200 37399 62 6351 6426 13185 13973 16699 22524 31070 31916 63 4098 10617 14854 18004 28580 36158 37500 38552

In another example, when the length N of the LDPC codeword is 16200 and the code rate is 6/15, the indexes of rows where 1 is located in the 0^(th) column of the ith column group in the matrix A and the matrix C are defined as shown in Table 28 presented below:

TABLE 28 Indexes of rows where 1 is located in i the 0th column of the ith column group 0 15 593 1066 1714 5358 6168 7077 7979 1 339 731 769 1399 4678 7100 8114 8696 2 247 344 510 5273 5668 6136 8569 9147 3 21 283 521 4055 4548 4957 6557 7718 4 3 110 880 1410 4143 8297 9105 9115 5 2 559 636 1934 2947 3765 4060 5072 6 741 754 1040 1827 2112 3338 4693 6498 7 213 338 775 2464 2974 3852 4353 4787 8 211 428 432 2439 2694 4541 6025 8071 9 28 239 855 2060 3791 7217 8722 10 407 555 814 2635 3037 4619 8473 11 203 846 988 2599 4890 7749 9671 12 641 632 801 2577 4612 4916 5286 13 111 577 728 2998 4109 5547 8002 14 197 391 480 1526 9016 9434 9447 15 382 446 546 3865 6824 7752 8076 16 307 321 1031 4476 7858 8463 9604 17 112 252 446 1665 2189 4869 5570 18 4566 6695 7966 8371 9608 19 2490 3419 6716 9038 9232 20 1117 1203 6031 7193 7320

In another example, when the length N of the LDPC codeword is 64800 and the code rate is 6/15, the indexes of rows where 1 is located in the 0^(th) column of the ith column group in the matrix A and the matrix C are defined as shown in Table 29 presented below:

TABLE 29 Index of row where 1 is located in I the 0th column of the ith column group 0 71 276 856 6867 12964 17373 18159 26420 28460 28477 1 257 322 672 2533 5316 6578 9037 10231 13845 36497 2 233 765 904 1366 3875 13145 15409 18620 23910 30825 3 100 224 405 12776 13868 14787 16781 23886 29099 31419 4 23 496 891 2512 12589 14074 19392 20339 27658 28684 5 473 712 759 1283 4374 9898 12551 13814 24242 32728 6 511 567 815 11823 17106 17900 19338 22315 24396 26448 7 45 733 836 1923 3727 17468 25746 33806 35995 36657 8 17 487 675 2670 3922 5145 18009 23993 31073 36624 9 72 751 773 1937 17324 28512 30666 30934 31016 31849 10 257 343 594 14041 19141 24914 26864 28809 32055 34753 11 99 241 491 2650 9670 17433 17785 18988 22235 30742 12 198 299 655 6737 8304 10917 16092 19387 20755 37690 13 351 916 926 18151 21708 23216 30321 33578 34052 37949 14 54 332 373 2010 3332 5623 16301 34337 36451 37861 15 139 257 1068 11090 20289 29694 29732 32640 35133 36404 16 457 855 968 2155 4956 5422 5949 17570 26673 32387 17 137 570 619 5006 6099 7979 14429 16650 25443 32789 18 46 282 287 10258 18383 20258 27186 27494 28429 38266 19 445 486 1058 1868 9976 11294 20364 23695 30826 35330 20 134 900 931 12518 14544 17715 19623 21111 33668 34570 21 65 66 586 8020 20270 23831 31041 31965 32224 35189 22 174 290 784 6740 14673 17642 26286 27382 33447 34879 23 332 675 1033 1838 12004 15439 20765 31721 34225 38863 24 527 558 832 3867 6318 8317 10883 13466 18427 25377 25 431 780 1021 1112 2873 7675 13059 17793 20570 20771 26 339 536 1015 5725 6916 10846 14487 21156 28123 32614 27 456 830 1078 7511 11801 12362 12705 17401 28867 34032 28 222 538 989 5593 6022 8302 14008 23445 25127 29022 29 37 393 788 3025 7768 11367 22276 22761 28232 30394 30 234 257 1045 1307 2908 6337 26530 28142 34129 35997 31 35 46 978 9912 9978 12567 17843 24194 34887 35206 32 39 959 967 5027 10847 14657 18859 28075 28214 36325 33 275 477 823 11376 18073 28997 30521 31661 31941 32116 34 185 580 966 11733 12013 12760 13358 19372 32534 35504 35 760 891 1046 11150 20358 21638 29930 31014 33050 64840 36 360 389 1057 5316 5938 14186 16404 32445 34021 35722 37 306 344 679 5224 6674 10305 18753 25583 30585 36943 38 103 171 1016 8780 11741 12144 19470 20955 22495 27377 39 818 832 894 3883 14279 14497 22505 26129 28719 31246 40 215 411 760 5886 25612 28556 32213 32704 35901 36130 41 229 489 1067 2385 8587 20565 23431 28102 30147 32859 42 288 664 980 8138 8531 21676 23787 26708 28798 34490 43 89 552 847 6656 9889 23949 26226 27080 31236 35823 44 66 142 443 3339 3913 7977 14944 15464 19186 25983 45 605 876 931 16682 17669 25800 28220 33432 35738 37382 46 346 423 806 5669 7668 8789 9928 19724 24039 27893 47 48 460 1055 3512 7389 7549 20216 22180 28221 35437 48 187 636 824 1678 4508 13588 19683 21750 30311 33480 49 25 768 935 2856 8187 9052 21850 29941 33217 34293 50 349 624 716 2698 6395 6435 8974 10649 15932 17378 51 336 410 871 3582 9830 10885 13892 18027 19203 36659 52 176 849 1078 17302 19379 27964 28164 28720 32557 35495 53 234 890 1075 9431 9605 9700 10113 11332 12679 24268 54 516 638 733 8851 19871 22740 25791 30152 32659 35568 55 253 830 879 2086 16885 22952 23765 25389 34656 37293 56 94 954 998 2003 3369 6870 7321 29856 31373 34888 57 79 350 933 4853 6252 11932 12058 21631 24552 24876 58 246 647 778 4036 10391 10656 13194 32335 32360 34179 59 149 339 436 6971 8356 8715 11577 22376 28684 31249 60 36 149 220 6936 18408 19192 19288 23063 28411 35312 61 273 683 1042 6327 10011 18041 21704 29097 30791 31425 62 46 138 722 2701 10964 13002 19930 26625 26456 28965 63 12 1009 1040 1990 2930 5302 21215 22625 23011 29288 64 125 241 819 2245 3199 8415 21133 26786 27226 38838 65 45 476 1075 7393 15141 20414 31244 3336 35004 38391 66 432 578 667 1343 10466 11314 11507 23314 27720 34465 67 248 291 556 1971 3989 8992 18000 19998 23932 34652 68 68 694 837 2246 7472 7873 11078 12868 20937 35591 69 272 924 949 2030 4360 6203 9737 19705 19902 38039 70 21 314 979 2311 2632 4109 19527 21920 31413 34277 71 197 253 804 1249 4315 10021 14358 20559 27099 30525 72 9802 16164 17499 22378 22403 22704 26742 29908 73 9064 10904 12305 14057 16156 26000 32613 34536 74 5178 6319 10239 19343 25628 30577 31110 32291

In another example, when the length N of the LDPC codeword is 16200 and the code rate is 7/15, the indexes of rows where 1 is located in the 0^(th) column of the ith column group in the matrix A and the matrix C are defined as shown in Table 30 presented below:

TABLE 30 Indexes of rows where 1 is located i in the 0th column of the ith column group 0 56 330 835 1133 1731 2171 5077 7762 1 21 259 845 1827 2503 3258 7361 7490 2 105 779 1069 1366 7074 7251 7294 7514 3 16 558 923 2455 4076 6294 7507 8475 4 37 197 384 2184 2223 6347 6525 7258 5 197 393 844 1961 3881 5842 6368 8032 6 374 588 1069 3093 4484 5868 7320 7 243 767 790 1603 1867 4804 7416 8 0 242 730 2141 4235 4642 5063 9 148 327 431 2291 3847 5133 7977 10 110 864 925 2730 4227 6604 7219 11 571 746 867 1384 3974 5944 6713 12 268 347 948 1515 3629 5598 7538 13 876 904 1049 4249 5198 6938 7701 14 690 748 782 1304 2117 4528 4589 15 14 300 703 2968 4571 6102 7754 16 832 998 1071 2591 3865 4812 6321 17 458 903 976 5179 5520 6862 8068 18 155 358 984 1417 1602 2697 3044 19 312 701 784 1636 2183 3501 5170 20 85 981 989 2893 2951 4457 4685 21 5091 5244 5293 5404 6009 22 2171 2203 2344 3255 6338 23 3072 4338 6965 7045 8061

In another example, when the length N of the LDPC codeword is 64800 and the code rate is 7/15, the indexes of rows where 1 is located in the 0^(th) column of the ith column group in the matrix A and the matrix C are defined as shown in Table 31 presented below:

TABLE 31 Indexes of rows where 1 is located i in the 0th column of the ith column group 0 460 792 1007 4580 11452 13130 26882 27020 32439 1 35 472 1056 7154 12700 13326 13414 16828 19102 2 45 440 772 4854 7863 26945 27684 28651 31875 3 744 812 892 1509 9018 12925 14140 21357 25106 4 271 474 761 4268 6706 9609 19701 19707 24870 5 223 477 662 1987 9247 18376 22148 24948 27694 6 44 379 786 8823 12322 14666 16377 28688 29924 7 104 219 562 5832 19665 20615 21043 22759 32180 8 41 43 870 7963 13718 14136 17216 30470 33428 9 592 744 887 4513 6192 18116 19482 25032 34095 10 456 821 1078 7162 7443 8774 15567 17243 33085 11 151 666 977 6946 10358 11172 18129 19777 32234 12 236 793 870 2001 6805 9047 13877 30131 34252 13 297 698 772 3449 4204 11608 22950 26071 27512 14 202 428 474 3205 3726 6223 7708 20214 25283 15 139 719 915 1447 2938 11864 15932 21748 28598 16 135 853 902 3239 18590 20579 30578 33374 34045 17 9 13 971 11834 13642 17628 21669 24741 30965 18 344 531 730 1880 16895 17587 21901 28620 31957 19 7 192 380 3168 3729 5518 6827 20372 34168 20 28 521 681 4313 7465 14209 21501 23364 25980 21 269 393 898 3561 11066 11985 17311 26127 30309 22 42 82 707 4880 4890 9618 23340 25959 31695 23 189 262 707 6573 14082 22259 24230 24390 24664 24 383 568 573 5498 13449 13990 16904 22629 34203 25 585 596 820 2440 2488 21956 28261 28703 29591 26 755 763 795 5636 16433 21714 23452 31150 34545 27 23 343 669 1159 3507 13096 17978 24241 34321 28 316 384 944 4872 8491 18913 21085 23198 24798 29 64 314 765 3706 7136 8634 14227 17127 23437 30 220 693 899 8791 12417 13487 18335 22126 27428 31 285 794 1045 8624 8801 9547 19167 21894 32657 32 386 621 1045 1634 1882 3172 13686 16027 22448 33 95 622 693 2827 7098 11452 14112 18831 31308 34 446 813 928 7976 8935 13146 27117 27766 33111 35 89 138 241 3218 9283 20458 31484 31538 34216 36 277 420 704 9281 12576 12788 14496 15357 20585 37 141 643 758 4894 10264 15144 16357 22478 26461 38 17 108 160 13183 15424 17939 19276 23714 26655 39 109 285 608 1682 20223 21791 24615 29622 31983 40 123 515 622 7037 13946 15292 15606 16262 23742 41 264 565 923 6460 13622 13934 23181 25475 26134 42 202 548 789 8003 10993 12478 16051 25114 27579 43 121 450 575 5972 10062 18693 21852 23874 28031 44 507 560 889 12064 13316 19629 21547 25461 28732 45 664 786 1043 9137 9294 10163 23389 31436 34297 46 45 830 907 10730 16541 21232 30354 30605 31847 47 203 507 1060 6971 12216 13321 17861 22671 29825 48 369 881 952 3035 12279 12775 17682 17805 34281 49 683 709 1032 3787 17623 24138 26775 31432 33626 50 524 792 1042 12249 14765 18601 25811 32422 33163 51 137 639 688 7182 8169 10443 22530 24597 29039 52 159 643 749 16386 17401 24135 28429 33468 33469 53 107 481 555 7322 13234 19344 23498 26581 31378 54 249 389 523 3421 10150 17616 19085 20545 32069 55 395 738 1045 2415 3005 3820 19541 23543 31068 56 27 293 703 1717 3460 8326 8501 10290 32625 57 126 247 515 6031 9549 10643 22067 29490 34450 58 331 471 1007 3020 3922 7580 23358 28620 30946 59 222 542 1021 3291 3652 13130 16349 33009 34348 60 532 719 1038 5891 7528 23252 25472 31395 31774 61 145 398 774 7816 13887 14936 23708 31712 33160 62 88 536 600 1239 1887 12195 13782 16726 27998 63 151 269 585 1445 3178 3970 15568 20358 21051 64 650 819 865 15567 18546 25571 32038 33350 33620 65 93 469 800 6059 10405 12296 17515 21354 22231 66 97 206 951 6161 16376 27022 29192 30190 30665 67 412 549 986 5833 10583 10766 24946 28878 31937 68 72 604 659 5267 12227 21714 32120 33472 33974 69 25 902 912 1137 2975 9642 11598 25919 28278 70 420 976 1055 8473 11512 20198 21662 25443 30119 71 1 24 932 6426 11899 13217 13935 16548 29737 72 53 618 988 6280 7267 11676 13575 15532 25787 73 111 739 809 8133 12717 12741 20253 20608 27850 74 120 683 943 14496 15162 15440 18660 27543 32404 75 600 754 1055 7873 9679 17351 27268 33508 76 344 756 1054 7102 7193 22903 24720 27883 77 582 1003 1046 11344 23756 27497 27977 32853 78 28 429 509 11106 11767 12729 13100 31792 79 131 555 907 5113 10259 10300 20580 23029 80 406 915 977 12244 20259 26616 27899 32228 81 46 195 224 1229 4116 10263 13608 17830 82 19 819 953 7965 9998 13959 30580 30754 83 164 1003 1032 12920 15975 16582 22624 27357 84 8433 11894 13531 17675 25889 31384 85 3166 3813 8596 10368 25104 29584 86 2466 8241 12424 13376 24837 32711

Hereinafter, positions of rows where 1 exists in the matrix A and the matrix C will be explained with reference to Table 24 by way of an example.

Since the length N of the LDPC codeword is 16200 and the code rate is 4/15 in Table 24, M₁=1080, M₂=10800, Q₁=3, and Q₂=30 in the parity check matrix 400 defined by Table 24 with reference to Table 22.

Herein, Q₁ is a size by which columns of the same column group are cyclic-shifted in the matrix A, and Q₂ is a size by which columns of the same column group are cyclic-shifted in the matrix C.

In addition, Q₁=M₁/L, Q₂=M₂/L, M₁=g, and M₂=N−K−g, and L is an interval at which a pattern of a column is repeated in the matrix A and the matrix C, and for example, may be 360.

The index of the row where 1 is located in the matrix A and the matrix C may be determined based on the M₁ value.

For example, since M₁=1080 in the case of Table 24, the positions of the rows where 1 exists in the 0^(th) column of the ith column group in the matrix A may be determined based on values smaller than 1080 from among the index values of Table 24, and the positions of the rows where 1 exists in the 0^(th) column of the ith column group in the matrix C may be determined based on values greater than or equal to 1080 from among the index values of Table 24.

Specifically, in Table 24, the sequence corresponding to the 0^(th) column group is “19, 585, 710, 3241, 3276, 3648, 6345, 9224, 9890, and 10841”. Accordingly, in the case of the 0^(th) column of the 0^(th) column group of the matrix A, 1 may be located in the 19^(th) row, 585^(th) row, and 710^(th) row, and, in the case of the 0^(th) column of the 0^(th) column group of the matrix C, 1 may be located in the 3241^(st) row, 3276^(th) row, 3648^(th) row, 6345^(th) row, 9224^(th) row, 9890^(th) row, and 10841^(st) row.

Once positions of 1 in the 0^(th) column of each column group of the matrix A are defined, positions of rows where 1 exists in another column of each column group may be defined by cyclic-shifting from the previous column by Q₁. Once positions of 1 in the 0^(th) column of each column group of the matrix C are defined, position of rows where 1 exists in another column of each column group may be defined by cyclic-shifting from the previous column by Q₂.

In the above-described example, in the case of the 0^(th) column of the 0^(th) column group of the matrix A, 1 exists in the 19^(th) row, 585^(th) row, and 710^(th) row. In this case, since Q₁=3, the indexes of rows where 1 exists in the 1^(st) column of the 0^(th) column group are 22(=19+3), 588(=585+3), and 713(=710+3), and the index of rows where 1 exists in the 2^(nd) column of the 0^(th) column group are 25(=22+3), 591 (=588+3), and 716(=713+3).

In the case of the 0^(th) column of the 0^(th) column group of the matrix C, 1 exists in the 3241^(st) row, 3276^(th) row, 3648^(th) row, 6345^(th) row, 9224^(th) row, 9890^(th) row, and 10841^(st) row. In this case, since Q₂=30, the index of rows where 1 exists in the 1^(st) column of the 0^(th) column group are 3271 (=3241+30), 3306(=3276+30), 3678 (=3648+30), 6375 (=6345+30), 9254 (=9224+30), 9920 (=9890+30), and 10871 (=10841+30), and the indexes of rows where 1 exists in the 2^(nd) column of the 0^(th) column group are 3301 (=3271+30), 3336(=3306+30), 3708 (=3678+30), 6405 (=6375+30), 9284 (=9254+30), 9950 (=9920+30), 10901 (=10871+30).

In this method, the positions of rows where 1 exists in all column groups of the matrix A and the matrix C are defined.

The matrix B may have a dual diagonal configuration, the matrix D may have a diagonal configuration (that is, the matrix D is an identity matrix), and the matrix Z may be a zero matrix.

As a result, the parity check matrix 400 shown in FIG. 4 may be defined by the matrices A, B, C, D, and Z having the above-described configurations.

Hereinafter, a method for performing LDPC encoding based on the parity check matrix 400 shown in FIG. 4 will be explained. An LDPC encoding process when the parity check matrix 400 is defined as shown in Table 24 by way of an example will be explained for the convenience of explanation.

For example, when an information word block S=(s₀, s₁, S_(K−1)) is LDPC-encoded, an LDPC codeword Λ=(λ₀, λ₁, . . . λ_(N−1))=(s₀, s₁, . . . S_(K−1), p₀, p₁, . . . , P_(M) ₁ _(+M) ₂ ⁻¹) including a parity bit P=(p₀, p₁, . . . , P_(M) ₁ _(+M) ₂ ⁻¹).

M₁ and M₂ indicate the size of the matrix B having the dual diagonal configuration and the size of the matrix C having the diagonal configuration, respectively, and M₁=g, M₂=N−K−g.

A process of calculating a parity bit is as follows. In the following explanation, the parity check matrix 400 is defined as shown in Table 24 by way of an example, for the convenience of explanation.

Step 1) λ and p are initialized as λ_(i)=s₁ (i=0, 1, . . . , K−1), p_(j)=0 (j=0, 1, . . . , M₁+M₂−1).

Step 2) The 0^(th) information word bit λ₀ is accumulated in the address of the parity bit defined in the first row (that is, the row of i=0) of Table 24. This may be expressed by Equation 12 presented below:

$\begin{matrix} {{P_{19} = {P_{19} \oplus \lambda_{0}}}{P_{585} = {P_{585} \oplus \lambda_{0}}}{P_{710} = {P_{710} \oplus \lambda_{0}}}{P_{3241} = {P_{3241} \oplus \lambda_{0}}}{P_{3276} = {P_{3276} \oplus \lambda_{0}}}{P_{3648} = {P_{3648} \oplus \lambda_{0}}}{P_{6345} = {P_{6345} \oplus \lambda_{0}}}{P_{9224} = {P_{9224} \oplus \lambda_{0}}}{P_{9890} = {P_{9890} \oplus \lambda_{0}}}{P_{10841} = {P_{10841} \oplus \lambda_{0}}}} & (12) \end{matrix}$

Step 3) Regarding the next L−1 number of information word bits λ_(m) (m=1, 2, . . . , L−1), λ_(m) is accumulated in the parity bit address calculated based on Equation 13 presented below: (χ+m×Q ₁)mod M ₁ (if χ<M ₁) M ₁+{(χM ₁ +m×Q ₂)mod M ₂} (if χ≥M ₁)  (13)

Herein, x is an address of a parity bit accumulator corresponding to the 0^(th) information word bit λ₀.

In addition, Q₁=M₁/L and Q₂=M₂/L. In addition, since the length N of the LDPC codeword is 16200 and the code rate is 4/15 in Table 24, M₁=1080, M₂=10080, Q₁=3, Q₂=30, and L=360 with reference to Table 22.

Accordingly, an operation as shown in Equation 14 presented below may be performed for the 1^(st) information word bit λ₁:

$\begin{matrix} {{P_{22} = {P_{22} \oplus \lambda_{1}}}{P_{588} = {P_{588} \oplus \lambda_{1}}}{P_{713} = {P_{713} \oplus \lambda_{1}}}{P_{3271} = {P_{3271} \oplus \lambda_{1}}}{P_{3306} = {P_{3306} \oplus \lambda_{1}}}{P_{3678} = {P_{3678} \oplus \lambda_{1}}}{P_{6375} = {P_{6375} \oplus \lambda_{1}}}{P_{9254} = {P_{9254} \oplus \lambda_{1}}}{P_{9920} = {P_{9920} \oplus \lambda_{1}}}{P_{10871} = {P_{10871} \oplus \lambda_{1}}}} & (14) \end{matrix}$

Step 4) Since the same address of the parity bit as in the second row (that is the row of i=1) of Table 24 is given to the Lth information word bit λ_(L), in a similar method to the above-described method, the address of the parity bit regarding the next L−1 number of information word bits λ_(m) (m=L+1, L+2, . . . , 2L−1) is calculated based on Equation 13. In this case, x is the address of the parity bit accumulator corresponding to the information word bit 4, and may be obtained based on the second row of Table 24.

Step 5) The above-described processes are repeated for L number of new information word bits of each group by considering new rows of Table 24 as the address of the parity bit accumulator.

Step 6) After the above-described processes are repeated for the codeword bits λ₀ to λ_(K−1), values regarding Equation 15 presented below are calculated in sequence from i=1: P _(i) =P _(i) ⊕P _(i−1)(i=1,2, . . . ,M ₁−1)  (15)

Step 7) Parity bits λ_(K) to λ_(K+M) ₁ ⁻¹ corresponding to the matrix B having the dual diagonal configuration are calculated based on Equation 16 presented below: λ_(K+L×t+s) =p _(Q) ₁ _(×S+t)(0≤s<L,0≤t<Q ₁)  (16)

Step 8) The address of the parity bit accumulator regarding L number of new codeword bits λ_(K) to λ_(K+M) ₁ ⁻¹ of each group is calculated based on Table 24 and Equation 13.

Step 9) After the codeword bits λ_(K) to λ_(K+M) ₁ ⁻¹ are calculated, parity bits λ_(K+M) ₁ to λ_(K+M) ₁ _(+M) ₂ ⁻¹ corresponding to the matrix C having the diagonal configuration are calculated based on Equation 17 presented below: λ_(K+M) ₁ _(+L×t+s) =p _(M) ₁ _(+Q) ₂ _(×S+t)(0≤s<L,0≤t<Q ₂)  (17)

As a result, the parity bits may be calculated in the above-described method.

Referring back to FIG. 1, the encoder 110 may perform the LDPC encoding by using various code rates such as 3/15, 4/15, 5/15, 6/15, 7/15, 8/15, 9/15, 10/15, 11/15, 12/15, 13/15, etc. In addition, the encoder 110 may generate an LDPC codeword having various lengths such as 16200, 64800, etc., based on the length of the information word bits and the code rate.

In this case, the encoder 110 may perform the LDPC encoding by using the parity check matrix, and the parity check matrix is configured as shown in FIGS. 2 to 4.

In addition, the encoder 110 may perform Bose, Chaudhuri, Hocquenghem (BCH) encoding as well as LDPC encoding. To achieve this, the encoder 110 may further include a BCH encoder (not shown) to perform BCH encoding.

In this case, the encoder 110 may perform encoding in an order of BCH encoding and LDPC encoding. Specifically, the encoder 110 may add BCH parity bits to input bits by performing BCH encoding and LDPC-encodes the information word bits including the input bits and the BCH parity bits, thereby generating the LDPC codeword.

The interleaver 120 interleaves the LDPC codeword. That is, the interleaver 120 receives the LDPC codeword from the encoder 110, and interleaves the LDPC codeword based on various interleaving rules.

In particular, the interleaver 120 may interleave the LDPC codeword such that a bit included in a predetermined bit group from among a plurality of bit groups constituting the LDPC codeword (that is, a plurality of groups or a plurality of blocks) is mapped onto a predetermined bit of a modulation symbol.

In this case, the interleaver 120 may interleave the LDPC codeword such that bits included in continuous bit groups from among the plurality of bit groups of the LDPC codeword are mapped onto the same modulation symbol.

In addition, when check nodes connected only to a single parity bit in the parity check matrix of the LDPC code exists in plurality number, the interleaver 120 may interleave the LDPC codeword such that bits included in the bit groups corresponding to the parity bit to which the check nodes are connected are selectively mapped onto the modulation symbol.

Accordingly, the modulator 130 may map the bit included in the predetermined bit group from among the plurality of bit groups of the LDPC codeword onto a predetermined bit of the modulation symbol.

That is, the modulator 130 may map the bits included in the continuous bit groups from among the plurality of bit groups of the LDPC codeword onto the same modulation symbol. In addition, when the check nodes connected only to a single parity bit in the parity check matrix of the LDPC code exists in plurality number, the modulator 130 may selectively map the bits included in the bit groups corresponding to the parity bit to which the check nodes are connected onto the same modulation symbol.

To achieve this, as shown in FIG. 5, the interleaver 120 may include a parity interleaver 121, a group interleaver (or a group-wise interleaver 122), a group twist interleaver 123 and a block interleaver 124.

The parity interleaver 121 interleaves the parity bits constituting the LDPC codeword.

Specifically, when the LDPC codeword is generated based on the parity check matrix 200 having the configuration of FIG. 2, the parity interleaver 121 may interleave only the parity bits of the LDPC codeword by using Equations 18 presented below: u _(i) =c _(i) for 0≤i<K _(ldpc), and u _(K) _(ldpc) _(+M·t+s) =c _(K) _(ldpc) _(+Q) _(ldpc) _(·s+t) for 0≤s<M,0≤t<Q _(ldpc)  (18),

where M is an interval at which a pattern of a column group is repeated in the information word submatrix 210, that is, the number of columns included in a column group (for example, M=360), and Q_(ldpc) is a size by which each column is cyclic-shifted in the information word submatrix 210. That is, the parity interleaver 121 performs parity interleaving with respect to the LDPC codeword c=(c₀, c₁, . . . , c_(N) _(ldpc) ⁻¹), and outputs U=(u₀, u₁, . . . , u_(N) _(ldpc) ⁻¹).

The LDPC codeword parity-interleaved in the above-described method may be configured such that a predetermined number of continuous bits of the LDPC codeword have similar decoding characteristics (cycle distribution, a degree of a column, etc.).

For example, the LDPC codeword may have the same characteristics on the basis of M number of continuous bits. Herein, M is an interval at which a pattern of a column group is repeated in the information word submatrix 210 and, for example, may be 360.

Specifically, a product of the LDPC codeword bits and the parity check matrix should be “0”. This means that a sum of products of the i^(th) LDPC codeword bit, c₁(i=0, 1, . . . , N_(ldpc)−1) and the i^(th) column of the parity check matrix should be a “0” vector. Accordingly, the i^(th) LDPC codeword bit may be regarded as corresponding to the i^(th) column of the parity check matrix.

In the case of the parity check matrix 200 of FIG. 2, M number of columns in the information word submatrix 210 belong to the same group and the information word submatrix 210 has the same characteristics on the basis of a column group (for example, the columns belonging to the same column group have the same degree distribution and the same cycle characteristic).

In this case, since M number of continuous bits in the information word bits correspond to the same column group of the information word submatrix 210, the information word bits may be formed of M number of continuous bits having the same codeword characteristics. When the parity bits of the LDPC codeword are interleaved by the parity interleaver 121, the parity bits of the LDPC codeword may be formed of M number of continuous bits having the same codeword characteristics.

However, regarding the LDPC codeword encoded based on the parity check matrix 300 of FIG. 3 and the parity check matrix 400 of FIG. 4, parity interleaving may not be performed. In this case, the parity interleaver 121 may be omitted.

The group interleaver 122 may divide the parity-interleaved LDPC codeword into a plurality of bit groups and rearrange the order of the plurality of bit groups in bit group wise (or bit group unit). That is, the group interleaver 122 may interleave the plurality of bit groups in bit group wise.

According to an exemplary embodiment, when the parity interleaver 121 is omitted, the group interleaver 122 may divide the LDPC codeword into a plurality of bit groups and rearrange the order of the plurality of bit groups in bit group wise.

To achieve this, the group interleaver 122 divides the parity-interleaved LDPC codeword into a plurality of bit groups by using Equation 19 or Equation 20 presented below.

$\begin{matrix} {\mspace{79mu}{X_{j} = {{\left\{ {{\left. u_{k} \middle| j \right. = \left\lfloor \frac{k}{360} \right\rfloor},{0 \leq k < N_{ldpc}}} \right\}\mspace{14mu}{for}\mspace{14mu} 0} \leq j < N_{group}}}} & (19) \\ {{X_{j} = {{\left\{ {\left. u_{k} \middle| {{360 \times j} \leq k < {360 \times \left( {j + 1} \right)}} \right.,{0 \leq k < N_{ldpc}}} \right\}\mspace{14mu}{for}\mspace{14mu} 0} \leq j < N_{group}}},} & (20) \end{matrix}$ where N_(group) is the total number of bit groups, X_(j) is the j^(th) bit group, and u_(k) is the k^(th) LDPC codeword bit input to the group interleaver 122. In addition,

$\left\lfloor \frac{k}{360} \right\rfloor$ is the largest integer below k/360.

Since 360 in these equations indicates an example of the interval M at which the pattern of a column group is repeated in the information word submatrix, 360 in these equations can be changed to M.

The LDPC codeword which is divided into the plurality of bit groups may be as shown in FIG. 6.

Referring to FIG. 6, the LDPC codeword is divided into the plurality of bit groups and each bit group is formed of M number of continuous bits. When M is 360, each of the plurality of bit groups may be formed of 360 bits. Accordingly, the bit groups may be formed of bits corresponding to the column groups of the parity check matrix.

Specifically, since the LDPC codeword is divided by M number of continuous bits, K_(ldpc) number of information word bits are divided into (K_(ldpc)/M) number of bit groups and N_(ldpc)−K_(ldpc) number of parity bits are divided into (N_(ldpc)−K_(ldpc))/M number of bit groups. Accordingly, the LDPC codeword may be divided into (N_(ldpc)/M) number of bit groups in total.

For example, when M=360 and the length N_(ldpc) of the LDPC codeword is 64800, the number of bit groups N_(groups) is 180(=64800/360), and, when the M=360 and the length N_(ldpc) of the LDPC codeword is 16200, the number of bit groups N_(group) is 45(=16200/360).

As described above, the group interleaver 122 divides the LDPC codeword such that M number of continuous bits are included in a same group since the LDPC codeword has the same codeword characteristics on the basis of M number of continuous bits. Accordingly, when the LDPC codeword is grouped by M number of continuous bits, the bits having the same codeword characteristics belong to the same group.

In the above-described example, the number of bits constituting each bit group is M. However, this is merely an example and the number of bits constituting each bit group is variable.

For example, the number of bits constituting each bit group may be an aliquot part of M. That is, the number of bits constituting each bit group may be an aliquot part of the number of columns constituting a column group of the information word submatrix of the parity check matrix. In this case, each bit group may be formed of aliquot part of M number of bits. For example, when the number of columns constituting a column group of the information word submatrix is 360, that is, M=360, the group interleaver 122 may divide the LDPC codeword into a plurality of bit groups such that the number of bits constituting each bit group is one of the aliquot parts of 360.

In the following explanation, the number of bits constituting a bit group is M by way of an example, for the convenience of explanation.

Thereafter, the group interleaver 122 interleaves the LDPC codeword in bit group wise. Specifically, the group interleaver 122 may group the LDPC codeword into the plurality of bit groups and rearrange the plurality of bit groups in bit group wise. That is, the group interleaver 122 changes positions of the plurality of bit groups constituting the LDPC codeword and rearranges the order of the plurality of bit groups constituting the LDPC codeword in bit group wise.

Herein, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise such that bit groups including bits mapped onto the same modulation symbol from among the plurality of bit groups are spaced apart from one another at predetermined intervals.

In this case, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by considering at least one of the number of rows and columns of the block interleaver 124, the number of bit groups of the LDPC codeword, and the number of bits included in each bit group, such that bit groups including bits mapped onto the same modulation symbol are spaced apart from one another at predetermined intervals.

To achieve this, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by using Equation 21 presented below: Y _(j) =X _(π(j))(0≤j<N _(group))  (21),

where X_(j) is the j^(th) bit group before group interleaving, and Y_(j) is the j^(th) bit group after group interleaving. In addition, π(j) is a parameter indicating an interleaving order and is determined by at least one of a length of an LDPC codeword, a modulation method, and a code rate. That is, π(j) denotes a permutation order for group wise interleaving.

Accordingly, X_(π(j)) is a π(j)^(th) bit group before group interleaving, and Equation 21 means that the pre-interleaving π(j)^(th) bit group is interleaved into the j^(th) bit group.

According to an exemplary embodiment, an example of π(j) may be defined as in Tables 32 to 56 presented below.

In this case, π(j) is defined according to a length of an LPDC codeword and a code rate, and a parity check matrix is also defined according to a length of an LDPC codeword and a code rate. Accordingly, when LDPC encoding is performed based on a specific parity check matrix according to a length of an LDPC codeword and a code rate, the LDPC codeword may be interleaved in bit group wise based on π(j) satisfying the corresponding length of the LDPC codeword and code rate.

For example, when the encoder 110 performs LDPC encoding at a code rate of 7/15 to generate an LDPC codeword of a length of 16200, the group interleaver 122 may perform interleaving by using π(j) which is defined according to the length of the LDPC codeword of 16200 and the code rate of 7/15 in Tables 32 to 56 presented below.

For example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 5/15, and the modulation method (or modulation format) is Quadrature Phase Shift Keying (QPSK), π(j) may be defined as in Table 32 presented below. In particular, Table 32 may be applied when LDPC encoding is performed based on the parity check matrix defined by Table 26.

TABLE 32 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) j-th block  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 of Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 interleaver output π(j)-th block of 35  7 29 11 14 32 38 28 20 17 25 39 19  4  1 12 10 30  0 44 43  2 21 Group-wise  5 13 34 37 23 15 36 18 42 16 33 31 27 22  3  6 40 24 41  9 26  8 interleaver input

In the case of Table 32, Equation 21 may be expressed as Y₀=X_(π(0))=X₃₅, Y₁=X_(π(1))=X₇, Y₂=X_(π(2))=X₂₉, . . . , Y₄₃=X_(π(43))=X₂₆, and Y₄₄=X_(π(44))=X₈. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 35^(th) bit group to the 0^(th) bit group, the 7^(th) bit group to the 1^(st) bit group, the 29^(th) bit group to the 2^(nd) bit group, . . . , the 26^(th) bit group to the 43^(rd) bit group, and the 8^(th) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 7/15, and the modulation method is QPSK, π(j) may be defined as in Table 33 presented below. In particular, Table 33 may be applied when LDPC encoding is performed based on the parity check matrix defined by Table 6.

TABLE 33 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) j-th block  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 of Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 interleaver output π(j)-th block of  4 22 23 44 34  1  3  2 32 42  6 15 30 40 18  5 28 38  7 14 26 36  9 Group-wise  0 16 43 33 17 11 12 31 41 21 20 29 39 10 24 27 37 13 19 25 35  8 interleaver input

In the case of Table 33, Equation 21 may be expressed as Y₀=X_(π(0))=X₄, Y₁=X_(π(1))=X₂₂, Y₂=X_(π(2))=X₂₃, . . . , Y₄₃=X_(π(43))=X₃₅, and Y₄₄=X_(π(44))=X₈. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 4^(th) bit group to the 0^(th) bit group, the 22^(nd) bit group to the 1^(st) bit group, the 23^(rd) bit group to the 2^(nd) bit group, . . . , the 35^(th) bit group to the 43^(rd) bit group, and the 8^(th) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 9/15, and the modulation method is QPSK, π(j) may be defined as in Table 34 presented below. In particular, Table 34 may be applied when LDPC encoding is performed based on the parity check matrix defined by Table 8.

TABLE 34 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) j-th block  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 of Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 interleaver output π(j)-th block of 28 16 13 42 32 22 14 20 36 26  6  4 40 30  8  9 44 34 24 10 17 38 27 Group-wise 12 19 41 31 21  1 15 35 25  2  0 39 29  3  5 43 33 23  7 11 37 18 interleaver input

In the case of Table 34, Equation 21 may be expressed as Y₀=X_(π(0))=X₂₈, Y₁=X_(π(1))=X₁₆, Y₂=X_(π(2))=X₁₃, . . . , Y₄₃=X_(π(43))=X₃₇, and Y₄₄=X_(π(44))=X₁₈. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 28^(th) bit group to the 0^(th) bit group, the 16^(th) bit group to the 1^(st) bit group, the 13^(th) bit group to the 2^(nd) bit group, . . . , the 37^(th) bit group to the 43^(rd) bit group, and the 18^(th) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 11/15, and the modulation method is QPSK, π(j) may be defined as in Table 35 presented below. In particular, Table 35 may be applied when LDPC encoding is performed based on the parity check matrix defined by Table 10.

TABLE 35 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) j-th block  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 of Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 interleaver output π(j)-th block of  1  2 40 14 27 24 36  7  9 11 12 42 18 17 28 38 31  5 32 34 44 23  0 Group-wise 25 39 26 10 29 35  8 15 16 13 41  3  6  4 37 19 22 20 33 43 30 21 interleaver input

In the case of Table 35, Equation 21 may be expressed as Y₀=X_(π(0))=X₁, Y₁=X_(π(1))=X₂, Y₂=X_(π(2))=X₄₀, . . . , Y₄₃=X_(π(43))=X₃₀, and Y₄₄=X_(π(44))=X₂₁. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 1^(st) bit group to the 0^(th) bit group, the 2^(nd) bit group to the 1^(st) bit group, the 40^(th) bit group to the 2^(nd) bit group, . . . , the 30^(th) bit group to the 43^(rd) bit group, and the 21^(st) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 13/15, and the modulation method is QPSK, π(j) may be defined as in Table 36 presented below. In particular, Table 36 may be applied when LDPC encoding is performed based on the parity check matrix defined by Table 12.

TABLE 36 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) j-th block  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 of Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 interleaver output π(j)-th block of 26 10 12 38 28 15  0 44 34 24 14  8 40 30 20 13 42 32 22 11  9 36 25 Group-wise  7  5 37 27  4 16 43 33 23  2 18 39 29 19  6 41 31 21  3 17 35  1 interleaver input

In the case of Table 36, Equation 21 may be expressed as Y₀=X_(π(0))=X₂₆, Y₁=X_(π(1))=X₁₀, Y₂=X_(π(2))=X₁₂, . . . , Y₄₃=X_(π(43))=X₃₅, and Y₄₄=X_(π(44))=X₁. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 26^(th) bit group to the 0^(th) bit group, the 10^(th) bit group to the 1^(st) bit group, the 12^(th) bit group to the 2^(nd) bit group, . . . , the 35^(th) bit group to the 43^(rd) bit group, and the 1^(st) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 5/15, and the modulation method is QPSK, π(j) may be defined as in Table 37 presented below. In particular, Table 37 may be applied when LDPC encoding is performed based on the parity check matrix defined by Table 4.

TABLE 37 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) j-th block  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 of Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 interleaver output π(j)-th block of  5 20 30 40 12 18 28 38  1  7 24 34 44  2 22 32 42 10  8 26 36 14 13 Group-wise 19 29 39  9 17 27 37 15  3 23 33 43 16 21 31 41  0  4 25 35 11  6 interleaver input

In the case of Table 37, Equation 21 may be expressed as Y₀=X_(π(0))=X₅, Y₁=X_(π(1))=X₂₀, Y₂=X_(π(2))=X₃₀, . . . , Y₄₃=X_(π(43))=X₁₁, and Y₄₄=X_(π(44))=X₆. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 5^(th) bit group to the 0^(th) bit group, the 20^(th) bit group to the 1^(st) bit group, the 30^(th) bit group to the 2^(nd) bit group, . . . , the 11^(th) bit group to the 43^(rd) bit group, and the 6^(th) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 7/15, and the modulation method is QPSK, π(j) may be defined as in Table 38 presented below. In particular, Table 38 may be applied when LDPC encoding is performed based on the parity check matrix defined by Table 5.

TABLE 38 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) j-th block  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 of Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 interleaver output π(j)-th block of 26 10 12 38 28 15  0 44 34 24 14  8 40 30 20 13 42 32 22 11  9 36 25 Group-wise  7  5 37 27  4 16 43 33 23  2 18 39 29 19  6 41 31 21  3 17 35  1 interleaver input

In the case of Table 38, Equation 21 may be expressed as Y₀=X_(π(0))=X₂₆, Y₁=X_(π(1))=X₁₀, Y₂=X_(π(2))=X₁₂, . . . , Y₄₃=X_(π(43))=X₃₅, and Y₄₄=X_(π(44))=X₁. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 26^(th) bit group to the 0^(th) bit group, the 10^(th) bit group to the 1^(st) bit group, the 12^(th) bit group to the 2^(nd) bit group, . . . , the 35^(th) bit group to the 43^(rd) bit group, and the 1^(st) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 9/15, and the modulation method is QPSK, π(j) may be defined as in Table 39 presented below. In particular, Table 39 may be applied when LDPC encoding is performed based on the parity check matrix defined by Table 7.

TABLE 39 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) j-th block  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 of Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 interleaver output π(j)-th block of  4 22 23 44 34  1  3  2 32 42  6 15 30 40 18  5 28 38  7 14 26 36  9 Group-wise  0 16 43 33 17 11 12 31 41 21 20 29 39 10 24 27 37 13 19 25 35  8 interleaver input

In the case of Table 39, Equation 21 may be expressed as Y₀=X_(π(0))=X₄, Y₁=X_(π(1))=X₂₂, Y₂=X_(π(2))=X₂₃, . . . , Y₄₃=X_(π(43))=X₃₅, and Y₄₄=X_(π(44))=X₈. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 4^(th) bit group to the 0^(th) bit group, the 22^(nd) bit group to the 1^(st) bit group, the 23^(rd) bit group to the 2^(nd) bit group, . . . , the 35^(th) bit group to the 43^(rd) bit group, and the 8^(th) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 11/15, and the modulation method is QPSK, π(j) may be defined as in Table 40 presented below. In particular, Table 40 may be applied when LDPC encoding is performed based on the parity check matrix defined by Table 9.

TABLE 40 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) j-th block  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 of Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 interleaver output π(j)-th block of  4 22 23 44 34  1  3  2 32 42  6 15 30 40 18  5 28 38  7 14 26 36  9 Group-wise  0 16 43 33 17 11 12 31 41 21 20 29 39 10 24 27 37 13 19 25 35  8 interleaver input

In the case of Table 40, Equation 21 may be expressed as Y₀=X_(π(0))=X₄, Y₁=X_(π(1))=X₂₂, Y₂=X_(π(2))=X₂₃, . . . , Y₄₃=X_(π(43))=X₃₅, and Y₄₄=X_(π(44))=X₈. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 4^(th) bit group to the 0^(th) bit group, the 22^(nd) bit group to the 1^(st) bit group, the 23^(rd) bit group to the 2^(nd) bit group, . . . , the 35^(th) bit group to the 43^(rd) bit group, and the 8^(th) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 13/15, and the modulation method is QPSK, π(j) may be defined as in Table 41 presented below. In particular, Table 41 may be applied when LDPC encoding is performed based on the parity check matrix defined by Table 11.

TABLE 41 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) j-th block  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 of Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 interleaver output π(j)-th block of  6  3 30 40  9 11 28 38 22  7 24 34 44 13  8 32 42  1 12 26 36  0 10 Group-wise 15 29 39 17 19 27 37  2  4 23 33 43 20 21 31 41 14 18 25 35 16  5 interleaver input

In the case of Table 41, Equation 21 may be expressed as Y₀=X_(π(0))=X₆, Y₁=X_(π(1))=X₃, Y₂=X_(π(2))=X₃₀, . . . , Y₄₃=X_(π(43))=X₁₆, and Y₄₄=X_(π(44))=X₅. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 6^(th) bit group to the 0^(th) bit group, the 3^(rd) bit group to the 1^(st) bit group, the 30^(th) bit group to the 2^(nd) bit group, . . . , the 16^(th) bit group to the 43^(rd) bit group, and the 5^(th) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 7/15, and the modulation method is QPSK, π(j) may be defined as in Table 42 presented below. In particular, Table 42 may be applied when LDPC encoding is performed based on the parity check matrix defined by Table 6.

TABLE 42 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) j-th block  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 of Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 interleaver output π(j)-th block of  3 22  7 18  6  1  4 14  5 15  2 23 26 28 30 32 34 36 10 38 21 44  9 Group-wise  0 33 40 42 17 11 19 24 20 12 16 25 27 29 31 13 35 37 39 41 43  8 interleaver input

In the case of Table 42, Equation 21 may be expressed as Y₀=X_(π(0))=X₃, Y₁=X_(π(1))=X₂₂, Y₂=X_(π(2))=X₇, . . . , Y₄₃=X_(π(43))=X₄₃, and Y₄₄=X_(π(44))=X₈. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 3^(rd) bit group to the 0^(th) bit group, the 22^(nd) bit group to the 1^(st) bit group, the 7^(th) bit group to the 2^(nd) bit group, . . . , the 43^(rd) bit group to the 43^(rd) bit group, and the 8^(th) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 5/15, and the modulation method is QPSK, π(j) may be defined as in Table 43 presented below.

TABLE 43 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) j-th block  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 of Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 interleaver output π(j)-th block of 28 20  8 39 21 25 22 17 29 38 15  7 43 24 11 35 30 27 14 10  6  9 13 Group-wise 42 40 23 36 31  3 34  1 41  2 18 44 19  0 37 26 12 32  4 33 16  5 interleaver input

In the case of Table 43, Equation 21 may be expressed as Y₀=X_(π(0))=X₂₈, Y₁=X_(π(1))=X₂₀, Y₂=X_(π(2))=X₈, . . . , Y₄₃=X_(π(43))=X₁₆, and Y₄₄=X_(π(44))=X₅. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 28^(th) bit group to the 0^(th) bit group, the 20^(th) bit group to the 1^(st) bit group, the 8^(th) bit group to the 2^(nd) bit group, . . . , the 16^(th) bit group to the 43^(rd) bit group, and the 5^(th) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 6/15, and the modulation method is QPSK, π(j) may be defined as in Table 44 presented below.

TABLE 44 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) j-th block  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 of Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 interleaver output π(j)-th block of 36  2 31 18 13  6 40 43 29 26 22 41 12 25 34 35 30  3 20 27 44 37 39 Group-wise  1 33 24 28  5 42 17 21 15  9 38 32 10 23  7  0 11 19 14  8  4 16 interleaver input

In the case of Table 44, Equation 21 may be expressed as Y₀=X_(π(0))=X₃₆, Y₁=X_(π(1))=X₂, Y₂=X_(π(2))=X₃₁, . . . , Y₄₃=X_(π(43))=X₄, and Y₄₄=X_(π(44))=X₁₆. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 36^(th) bit group to the 0^(th) bit group, the 2^(nd) bit group to the 1^(st) bit group, the 31^(st) bit group to the 2^(nd) bit group, . . . , the 4^(th) bit group to the 43^(rd) bit group, and the 16^(th) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 7/15, and the modulation method is QPSK, π(j) may be defined as in Table 45 presented below.

TABLE 45 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) j-th block  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 of Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 interleaver output π(j)-th block of 12 39 21 17 11  0 24 26 16 40 22  5 36 20 41 32 33 19 44  7 15 23 30 Group-wise 43  9 14  4  8 25  6 35 37 13 29 10  1 18 28 38 42 31  3 27 34  2 interleaver input

In the case of Table 45, Equation 21 may be expressed as Y₀=X_(π(0))=X₁₂, Y₁=X_(π(1))=X₃₉, Y₂=X_(π(2))=X₂₁, . . . , Y₄₃=X_(π(43))=X₃₄, and Y₄₄=X_(π(44))=X₂. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 12^(th) bit group to the 0^(th) bit group, the 39^(th) bit group to the 1^(st) bit group, the 21^(st) bit group to the 2^(nd) bit group, . . . , the 34^(th) bit group to the 43^(rd) bit group, and the 2^(nd) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 16200, the code rate is 9/15, and the modulation method is QPSK, π(j) may be defined as in Table 46 presented below.

TABLE 46 Order of bits group to be block interleaved π(j) (0 ≤ j < 45) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 interleaver output π(j)-th block of 41 37 26 22 32 9 23 21 8 4 25 15 10 17 19 16 2 6 36 3 30 24 1 Group-wise 29 13 5 0 34 27 42 12 33 43 28 35 40 14 44 11 18 7 31 20 39 38 interleaver input

In the case of Table 46, Equation 21 may be expressed as Y₀=X_(π(0))=X₄₁, Y₁=X_(π(1))=X₃₇, Y₂=X_(π(2))=X₂₆, . . . , Y₄₃=X_(π(43))=X₃₉, and Y₄₄=X_(π(44))=X₃₈. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 41^(st) bit group to the 0^(th) bit group, the 37^(th) bit group to the 1^(st) bit group, the 26^(th) bit group to the 2^(nd) bit group, . . . , the 39^(th) bit group to the 43^(rd) bit group, and the 38^(th) bit group to the 44^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 5/15, and the modulation method is QPSK, π(j) may be defined as in Table 47 presented below.

TABLE 47 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 π(j)-th block of 120 75 171 13 147 56 97 134 41 87 150 23 109 2 178 77 62 148 130 50 96 34 18 Group wise 115 4 159 81 169 71 136 149 94 39 21 110 121 60 8 174 73 131 142 157 40 24 107 interleaver 86 117 3 54 68 175 140 154 164 16 28 100 82 42 119 65 179 143 132 5 17 162 104 input 92 52 76 118 176 27 66 38 151 1 138 103 91 128 116 51 26 170 11 36 67 145 79 98 127 112 155 48 25 173 15 64 137 37 84 126 95 153 74 105 163 7 58 47 31 141 129 89 19 152 72 106 165 59 6 46 33 133 85 177 146 122 22 69 167 0 111 55 99 45 12 32 83 125 139 158 70 168 57 113 102 44 30 88 123 20 9 78 166 61 144 101 49 456 35 124 114 10 90 172 63 135 80 53 150 29 43 108 14 93 161

In the case of Table 47, Equation 21 may be expressed as Y₀=X_(π(0))=X₁₂₀, Y₁=X_(π(1))=X₇₅, Y₂=X_(π(2))=X₁₇₁, . . . , Y₁₇₈=X_(π(178))=X₉₃, and Y_(π(179))=X_(π(179))=X₁₆₁. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 120^(th) bit group to the 0^(th) bit group, the 75^(th) bit group to the 1^(st) bit group, the 171^(st) bit group to the 2^(nd) bit group, . . . , the 93^(rd) bit group to the 178^(th) bit group, and the 161^(st) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is QPSK, π(j) may be defined as in Table 48 presented below.

TABLE 48 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 π(j)-th block of 92 79 168 44 15 63 147 109 157 26 136 94 124 2 42 14 64 176 105 155 92 144 86 Group-wise 116 133 24 38 65 9 167 102 156 55 177 112 128 28 76 45 142 4 89 99 60 175 153 interleaver 118 35 19 129 46 139 6 81 70 179 151 95 57 18 115 30 169 41 135 78 125 148 104 input 62 16 91 29 161 40 3 174 51 73 123 113 61 84 97 13 34 138 172 158 0 23 71 47 59 83 117 98 134 146 170 7 159 27 69 43 88 58 101 121 140 17 111 1 178 75 166 87 37 54 126 150 12 22 114 103 72 160 82 93 50 171 33 137 149 11 107 127 21 77 96 66 162 36 48 145 10 108 119 25 131 85 67 163 173 49 141 39 106 152 5 122 90 20 74 164 56 132 32 110 143 100 8 120 154 80 68 53 130 31 165

In the case of Table 48, Equation 21 may be expressed as Y₀=X_(π(0))=X₉₂, Y₁=X_(π(1))=X₇₉, Y₂=X_(π(2))=X₁₆₈, . . . , Y₁₇₈=X_(π(178))=X₃₁, and Y₁₇₉=X_(π(179))=X₁₆₅. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 92^(nd) bit group to the 0^(th) bit group, the 79^(th) bit group to the 1^(st) bit group, the 168^(th) bit group to the 2^(nd) bit group, . . . , the 31^(st) bit group to the 178^(th) bit group, and the 165^(th) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is QPSK, π(j) may be defined as in Table 49 presented below.

TABLE 49 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 6 176 177 178 179 π(j)-th block of 53 65 29 159 39 13 134 148 108 120 85 174 75 54 164 1 21 44 95 130 144 118 154 Group-wise 33 76 58 106 167 11 96 0 23 136 151 177 78 60 42 122 165 102 92 12 24 147 179 interleaver 82 67 52 38 117 105 135 94 160 27 171 2 146 17 69 49 123 37 110 133 158 87 173 input 98 8 19 57 72 121 36 132 149 86 176 100 7 26 59 73 166 47 112 153 84 141 99 4 31 131 64 16 172 119 109 48 83 143 3 157 93 30 129 169 61 103 15 113 71 142 43 456 89 32 5 168 124 56 104 77 138 18 152 114 178 46 163 28 62 125 81 6 91 139 107 150 41 162 25 66 175 79 14 55 126 115 140 35 45 90 68 101 161 9 80 22 128 111 145 50 34 70 97 170 155 10 20 127 116 137 51 40 74 63 88

In the case of Table 49, Equation 21 may be expressed as Y₀=X_(π(0))=X₅₃, Y₁=X_(π(1))=X₆₅, Y₂=X_(π(2))=X₂₉, . . . , Y₁₇₈=X_(π(178))=X₆₃, and Y₁₇₉=X_(π(179))=X₈₈. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 53^(rd) bit group to the 0^(th) bit group, the 65^(th) bit group to the 1^(st) bit group, the 29^(th) bit group to the 2^(nd) bit group, . . . , the 63^(rd) bit group to the 178^(th) bit group, and the 88^(th) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is QPSK, π(j) may be defined as in Table 50 presented below.

TABLE 50 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 π(j)-th block of 18 169 30 63 155 132 99 1 87 117 145 73 179 19 56 167 43 32 128 156 112 4 89 Group-wise 140 69 14 100 49 34 168 151 120 0 89 110 136 64 13 74 45 170 160 125 149 91 111 interleaver 2 139 55 67 41 21 161 77 31 121 173 104 5 143 58 94 44 159 84 71 116 16 27 input 6 133 57 106 42 150 172 70 122 83 26 95 3 15 162 134 38 108 148 124 176 54 76 96 17 28 166 40 107 138 118 153 52 82 62 7 97 163 24 178 135 123 36 152 80 66 53 105 12 164 23 174 127 39 115 137 85 147 60 101 72 25 10 126 48 165 35 90 146 59 103 113 78 9 20 175 131 47 88 158 61 142 37 98 109 22 75 11 51 119 129 177 157 33 93 65 144 79 8 50 114 130 171 154 29 102 92 68 141 81 46

In the case of Table 50, Equation 21 may be expressed as Y₀=X_(π(0))=X₁₈, Y₁=X_(π(1))=X₁₆₉, Y₂=X_(π(2))=X₃₀, . . . , Y₁₇₈=X_(π(178))=X₈₁, and Y₁₇₉=X_(π(179))=X₄₆. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 18^(th) bit group to the 0^(th) bit group, the 169^(th) bit group to the 1^(st) bit group, the 30^(th) bit group to the 2^(nd) bit group, . . . , the 81^(st) bit group to the 178^(th) bit group, and the 46^(th) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is QPSK, π(j) may be defined as in Table 51 presented below.

TABLE 51 Order of bits group to be block interleaved π(j) (0 < j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 π(j)-th block of 18 169 30 63 155 132 99 1 87 117 145 73 179 19 56 167 43 32 128 156 112 4 89 Group-wise 140 69 14 100 49 34 168 151 120 0 86 110 136 64 13 74 45 170 160 125 149 91 111 interleaver 2 139 55 67 41 21 161 77 31 121 173 104 5 143 58 94 44 159 84 71 116 16 27 input 6 133 57 106 42 150 172 70 122 83 26 95 3 15 162 134 38 108 148 124 176 54 76 95 17 28 166 40 107 138 118 153 52 82 62 7 97 163 24 178 135 123 36 152 80 66 53 105 12 164 23 174 127 39 115 137 85 147 60 101 72 25 10 126 48 163 35 90 146 59 103 113 78 9 20 175 131 47 88 158 61 142 37 98 109 22 75 11 51 119 129 177 157 33 93 65 144 79 8 50 114 130 171 154 29 102 92 68 141 81 46

In the case of Table 51, Equation 21 may be expressed as Y₀=X_(π(0))=X₁₈, Y₁=X_(π(1))=X₁₆₉, Y₂=X_(π(2))=X₃₀, . . . , Y₁₇₈=X_(π(178))=X₈₁, and Y₁₇₉=X_(π(179))=X₄₆. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 18^(th) bit group to the 0^(th) bit group, the 169^(th) bit group to the 1^(st) bit group, the 30^(th) bit group to the 2^(nd) bit group, . . . , the 81^(st) bit group to the 178^(th) bit group, and the 46^(th) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is QPSK, π(j) may be defined as in Table 52 presented below.

TABLE 52 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 771 172 173 174 175 176 177 178 179 π(j)-th block of 18 169 30 63 155 132 99 1 87 117 145 73 179 19 56 167 43 32 128 156 112 4 89 Group-wise 140 69 14 100 49 34 168 151 120 0 86 110 136 64 13 74 45 170 160 125 149 91 111 interleaver 2 139 55 67 41 21 161 77 31 121 173 104 5 143 58 94 44 159 84 71 116 16 27 input 6 133 57 106 42 150 172 70 122 83 26 95 3 15 162 134 38 108 148 124 176 54 76 96 17 28 166 40 107 138 118 153 52 82 62 7 97 163 24 178 135 123 36 152 80 56 53 105 12 164 23 174 127 39 115 137 85 147 60 101 72 25 10 126 48 165 35 90 146 59 103 113 78 9 20 175 131 47 88 158 61 142 37 98 109 22 75 11 51 119 129 177 157 33 93 65 144 79 8 50 114 130 171 154 29 102 92 68 141 81 46

In the case of Table 52, Equation 21 may be expressed as Y₀=X_(π(0))=X₁₈, Y₁=X_(π(0))=X₁₆₉, Y₂=X_(π(2))=X₃₀, . . . , Y₁₇₈=X_(π(178))=X₈₁, and Y₁₇₉=X_(π(179))=X₄₆. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 18^(th) bit group to the 0^(th) bit group, the 169^(th) bit group to the 1^(st) bit group, the 30^(th) bit group to the 2^(nd) bit group, . . . , the 81^(st) bit group to the 178^(th) bit group, and the 46^(th) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is QPSK, π(j) may be defined as in Table 53 presented below.

TABLE 53 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 π(j)-th block of 43 150 26 119 108 7 173 163 81 135 71 45 153 55 92 125 16 115 32 177 105 67 140 Group-wise 79 54 4 126 154 20 166 37 112 95 64 144 76 48 5 134 124 25 160 176 88 59 100 interleaver 74 47 1 12 127 137 36 178 90 162 22 147 117 72 101 2 132 33 52 84 157 172 21 input 143 73 113 98 131 40 60 83 3 167 18 50 149 109 28 93 130 120 65 0 161 175 44 15 77 148 104 91 114 66 133 165 29 46 56 17 152 105 86 122 6 75 170 138 31 42 62 151 106 85 121 10 96 168 139 24 34 53 179 158 107 69 8 123 87 97 141 38 169 23 57 156 111 13 70 80 99 128 35 145 171 49 155 110 11 61 82 94 129 39 27 142 174 159 116 51 14 63 78 89 103 30 41 136 164 146 118 19 68 9 58

In the case of Table 53, Equation 21 may be expressed as Y₀=X_(π(0))=X₄₃, Y₁=X_(π(1))=X₁₅₀, Y₂=X_(π(2))=X₂₆, . . . , Y₁₇₈=X_(π(178))=X₉, and Y₁₇₉=X_(π(179))=X₅₈. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 43^(rd) bit group to the 0^(th) bit group, the 150^(th) bit group to the 1^(st) bit group, the 26^(th) bit group to the 2^(nd) bit group, . . . , the 9^(th) bit group to the 178^(th) bit group, and the 58^(th) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is QPSK, π(j) may be defined as in Table 54 presented below.

TABLE 54 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 π(j)-th block of 108 178 95 30 159 120 11 45 71 57 137 82 149 174 96 33 117 127 160 19 67 52 0 Group-wise 81 179 141 102 37 115 128 163 63 12 151 85 177 27 97 42 73 138 166 62 107 125 156 interleaver 15 25 89 176 40 51 145 77 114 61 99 162 28 129 7 17 39 152 86 74 140 53 175 input 101 123 2 13 31 165 88 155 143 41 59 110 132 70 9 24 171 91 122 146 48 36 106 161 136 14 75 60 94 173 3 119 47 148 109 29 133 84 16 66 167 6 121 49 157 104 26 144 134 93 72 169 1 38 55 116 103 18 153 142 83 126 65 8 172 50 32 100 21 111 154 78 139 124 68 168 90 56 35 4 22 150 113 135 46 79 69 38 164 58 34 5 147 118 23 44 130 80 92 105 64 170 54 10 158 20 43 131 76 87 112

In the case of Table 54, Equation 21 may be expressed as Y₀=X_(π(0))=X₁₀₈, Y₁=X_(π(1))=X₁₇₈, Y₂=X_(π(2))=X₉₅, . . . , Y₁₇₈=X_(π(178))=X₈₇, and Y₁₇₉=X_(π(179))=X₁₁₂. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 108^(th) bit group to the 0^(th) bit group, the 178^(th) bit group to the 1^(st) bit group, the 95^(th) bit group to the 2^(nd) bit group, . . . , the 87^(th) bit group to the 178^(th) bit group, and the 112^(th) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is QPSK, π(j) may be defined as in Table 55 presented below.

TABLE 55 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 π(j)-th block of 57 154 144 171 111 5 38 82 15 122 99 54 26 151 136 110 67 41 4 87 164 178 16 Group-wise 77 150 123 140 97 53 112 42 63 165 23 78 7 126 176 138 89 153 40 116 65 28 163 interleaver 52 106 2 131 83 147 12 177 95 32 167 44 59 114 73 84 139 149 124 13 27 101 0 input 61 113 174 91 74 50 157 134 20 35 1 64 102 169 118 75 46 158 128 141 36 3 18 100 86 56 172 71 160 119 145 43 29 11 96 107 133 173 85 68 159 143 49 37 24 117 6 130 179 80 66 104 142 166 48 17 33 92 120 132 79 156 62 109 175 51 14 39 90 121 137 25 72 161 103 148 58 10 47 93 127 115 22 34 70 162 152 60 8 105 45 129 81 94 30 19 170 146 69 9 55 108 135 125 98 31 88 21 168 155 76

In the case of Table 55, Equation 21 may be expressed as Y₀=X_(π(0))=X₅₇, Y₁=X_(π(1))=X₁₅₄, Y₂=X_(π(2))=X₁₄₄, . . . , Y₁₇₈=X_(π(178))=X₁₅₅, and Y₁₇₉=X_(π(179))=X₇₆. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 57^(th) bit group to the 0^(th) bit group, the 154^(th) bit group to the 1^(st) bit group, the 144^(th) bit group to the 2^(nd) bit group, . . . , the 155^(th) bit group to the 178^(th) bit group, and the 76^(th) bit group to the 179^(th) bit group.

In another example, when the length N_(ldpc) of the LDPC codeword is 64800, the code rate is 6/15, and the modulation method is QPSK, π(j) may be defined as in Table 56 presented below.

TABLE 56 Order of bits group to be block interleaved π(j) (0 ≤ j < 180) j-th block of 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Group-wise 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 interleaver 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 output 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 π(j)-th block of 127 38 14 83 58 72 107 150 0 179 117 138 161 22 44 82 32 100 56 5 60 120 133 Group-wise 168 17 157 147 87 104 39 4 60 29 121 131 15 172 156 73 142 43 95 106 59 119 85 interleaver 21 7 153 177 70 37 130 141 54 103 167 155 24 88 154 75 35 10 128 143 52 178 64 input 112 89 166 99 34 13 76 155 134 48 65 114 23 145 2 98 124 12 86 159 46 176 62 108 148 25 1 136 74 96 36 158 118 169 47 11 146 57 112 79 67 94 30 111 170 160 3 144 49 125 19 84 61 101 113 171 71 9 31 135 45 149 91 20 55 110 163 81 123 6 33 174 137 66 18 94 50 109 77 152 126 162 40 8 28 173 93 140 63 78 151 122 51 41 105 27 165 30 175 139 80 68 16 129 116 53 42 26 164 102 92

In the case of Table 56, Equation 21 may be expressed as Y₀=X_(π(0))=X₁₂₇, Y₁=X_(π(1))=X₃₈, Y₂=X_(π(2))=X₁₄, . . . , Y₁₇₈=X_(π(178))=X₁₀₂, and Y₁₇₉=X_(π(179))=X₉₂. Accordingly, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by changing the 127^(th) bit group to the 0^(th) bit group, the 38^(th) bit group to the 1^(st) bit group, the 14^(th) bit group to the 2^(nd) bit group, . . . , the 102^(nd) bit group to the 178^(th) bit group, and the 92^(nd) bit group to the 179^(th) bit group.

As described above, the group interleaver 122 may rearrange the order of the plurality of bit groups in bit group wise by using Equation 21 and Tables 32 to 56.

“j-th block of Group-wise Interleaver output” in Tables 32 to 56 indicates the j-th bit group output from the group interleaver 122 after interleaving, and “π(j)-th block of Group-wise Interleaver input” indicates the π(j)-th bit group input to the group interleaver 122.

In addition, since the order of the bit groups constituting the LDPC codeword is rearranged by the group interleaver 122 in bit group wise, and then the bit groups are block-interleaved by the block interleaver 124, which will be described below, “Order of bits groups to be block interleaved” is set forth in Tables 32 to 56 in relation to π(j).

The LDPC codeword which is group-interleaved in the above-described method is illustrated in FIG. 7. Comparing the LDPC codeword of FIG. 7 and the LDPC codeword of FIG. 6 before group interleaving, it can be seen that the order of the plurality of bit groups constituting wherein Q_(ldpc) is a cyclic shift parameter value regarding columns in a column group of an information word submatrix of the parity check matrix, N_(ldpc) is a length of the LDPC codeword, and K_(ldpc) is a length of information word bits of the LDPC codeword.

the LDPC codeword is rearranged.

That is, as shown in FIGS. 6 and 7, the groups of the LDPC codeword are arranged in order of bit group X₀, bit group X₁, . . . , bit group X_(Ngroup−1) before being group-interleaved, and are arranged in an order of bit group Y₀, bit group Y₁, . . . , bit group Y_(Ngroup−1) after being group-interleaved. In this case, the order of arranging the bit groups by the group interleaving may be determined based on Tables 32 to 56.

The group twist interleaver 123 interleaves bits in a same group. That is, the group twist interleaver 123 may rearrange the order of the bits in the same bit group by changing the order of the bits in the same bit group.

In this case, the group twist interleaver 123 may rearrange the order of the bits in the same bit group by cyclic-shifting a predetermined number of bits from among the bits in the same bit group.

For example, as shown in FIG. 8, the group twist interleaver 123 may cyclic-shift bits included in the bit group Y₁ to the right by 1 bit. In this case, the bits located in the 0^(th) position, the 1^(st) position, the 2^(nd) position, . . . , the 358^(th) position, and the 359^(th) position in the bit group Y₁ as shown in FIG. 8 are cyclic-shifted to the right by 1 bit. As a result, the bit located in the 359^(th) position before being cyclic-shifted is located in the front of the bit group Y₁ and the bits located in the 0^(th) position, the 1^(st) position, the 2^(nd) position, . . . , the 358^(th) position before being cyclic-shifted are shifted to the right serially by 1 bit and located.

In addition, the group twist interleaver 123 may rearrange the order of bits in each bit group by cyclic-shifting a different number of bits in each bit group.

For example, the group twist interleaver 123 may cyclic-shift the bits included in the bit group Y₁ to the right by 1 bit, and may cyclic-shift the bits included in the bit group Y₂ to the right by 3 bits.

However, the above-described group twist interleaver 123 may be omitted according to circumstances.

In addition, the group twist interleaver 123 is placed after the group interleaver 122 in the above-described example. However, this is merely an example. That is, the group twist interleaver 123 changes only the order of bits in a certain bit group and does not change the order of the bit groups. Therefore, the group twist interleaver 123 may be placed before the group interleaver 122.

The block interleaver 124 interleaves the plurality of bit groups the order of which has been rearranged. Specifically, the block interleaver 124 may interleave the plurality of bit groups the order of which has been rearranged by the group interleaver 122 in bit group wise (or bit group unit). The block interleaver 124 is formed of a plurality of columns each including a plurality of rows and may interleave by dividing the plurality of rearranged bit groups based on a modulation order determined according to a modulation method.

In this case, the block interleaver 124 may interleave the plurality of bit groups the order of which has been rearranged by the group interleaver 122 in bit group wise. Specifically, the block interleaver 124 may interleave by dividing the plurality of rearranged bit groups according to a modulation order by using a first part and a second part.

Specifically, the block interleaver 124 interleaves by dividing each of the plurality of columns into a first part and a second part, writing the plurality of bit groups in the plurality of columns of the first part serially in bit group wise, dividing the bits of the other bit groups into groups (or sub bit groups) each including a predetermined number of bits based on the number of columns, and writing the sub bit groups in the plurality of columns of the second part serially.

Herein, the number of bit groups which are interleaved in bit group wise may be determined by at least one of the number of rows and columns constituting the block interleaver 124, the number of bit groups and the number of bits included in each bit group. In other words, the block interleaver 124 may determine the bit groups which are to be interleaved in bit group wise considering at least one of the number of rows and columns constituting the block interleaver 124, the number of bit groups and the number of bits included in each bit group, interleave the corresponding bit groups in bit group wise, and divide bits of the other bit groups into sub bit groups and interleave the sub bit groups. For example, the block interleaver 124 may interleave at least part of the plurality of bit groups in bit group wise using the first part, and divide bits of the other bit groups into sub bit groups and interleave the sub bit groups using the second part.

Meanwhile, interleaving bit groups in bit group wise means that the bits included in the same bit group are written in the same column. In other words, the block interleaver 124, in case of bit groups which are interleaved in bit group wise, may not divide the bits included in the same bit groups and write the bits in the same column, and in case of bit groups which are not interleaved in bit group wise, may divide the bits in the bit groups and write the bits in different columns.

Accordingly, the number of rows constituting the first part is a multiple of the number of bits included in one bit group (for example, 360), and the number of rows constituting the second part may be less than the number of bits included in one bit group.

In addition, in all bit groups interleaved by the first part, the bits included in the same bit group are written and interleaved in the same column of the first part, and in at least one group interleaved by the second part, the bits are divided and written in at least two columns of the second part.

The specific interleaving method will be described later.

Meanwhile, the group twist interleaver 123 changes only the order of bits in the bit group and does not change the order of bit groups by interleaving. Accordingly, the order of the bit groups to be block-interleaved by the block interleaver 124, that is, the order of the bit groups to be input to the block interleaver 124, may be determined by the group interleaver 122. Specifically, the order of the bit groups to be block-interleaved by the block interleaver 124 may be determined by π(j) defined in Tables 32 to 56.

As described above, the block interleaver 124 may interleave the plurality of bit groups the order of which has been rearranged in bit group wise by using the plurality of columns each including the plurality of rows.

In this case, the block interleaver 124 may interleave the LDPC codeword by dividing the plurality of columns into at least two parts. For example, the block interleaver 124 may divide each of the plurality of columns into the first part and the second part and interleave the plurality of bit groups constituting the LDPC codeword.

In this case, the block interleaver 124 may divide each of the plurality of columns into N number of parts (N is an integer greater than or equal to 2) according to whether the number of bit groups constituting the LDPC codeword is an integer multiple of the number of columns constituting the block interleaver 124, and may perform interleaving.

When the number of bit groups constituting the LDPC codeword is an integer multiple of the number of columns constituting the block interleaver 124, the block interleaver 124 may interleave the plurality of bit groups constituting the LDPC codeword in bit group wise without dividing each of the plurality of columns into parts.

Specifically, the block interleaver 124 may interleave by writing the plurality of bit groups of the LDPC codeword on each of the columns in bit group wise in a column direction, and reading each row of the plurality of columns in which the plurality of bit groups are written in bit group wise in a row direction.

In this case, the block interleaver 124 may interleave by writing bits included in a predetermined number of bit groups which corresponds to a quotient obtained by dividing the number of bit groups of the LDPC codeword by the number of columns of the block interleaver 124 on each of the plurality of columns serially in a column direction, and reading each row of the plurality of columns in which the bits are written in a row direction.

Hereinafter, the group located in the j^(th) position after being interleaved by the group interleaver 122 will be referred to as group Y₃.

For example, it is assumed that the block interleaver 124 is formed of C number of columns each including R₁ number of rows. In addition, it is assumed that the LDPC codeword is formed of N_(group) number of bit groups and the number of bit groups N_(group) is a multiple of C.

In this case, when the quotient obtained by dividing N_(group) number of bit groups constituting the LDPC codeword by C number of columns constituting the block interleaver 124 is A (=N_(group)/C) (A is an integer greater than 0), the block interleaver 124 may interleave by writing A (=N_(group)/C) number of bit groups on each column serially in a column direction and reading bits written on each column in a row direction.

For example, as shown in FIG. 9, the block interleaver 124 writes bits included in bit group Y₀, bit group Y₁, . . . , bit group Y_(A−1) in the 1^(st) column from the 1^(st) row to the R₁ ^(th) row, writes bits included in bit group Y_(A), bit group Y_(A+1), . . . , bit group Y_(2A−1) in the 2nd column from the 1^(st) row to the R₁ ^(th) row, . . . , and writes bits included in bit group Y_(CA−A) bit group Y_(CA−A+1), . . . , bit group Y_(CA−1) in the column C from the 1^(st) row to the R₁ ^(th) row. The block interleaver 124 may read the bits written in each row of the plurality of columns in a row direction.

Accordingly, the block interleaver 124 interleaves all bit groups constituting the LDPC codeword in bit group wise.

However, when the number of bit groups of the LDPC codeword is not an integer multiple of the number of columns of the block interleaver 124, the block interleaver 124 may divide each column into 2 parts and interleave a part of the plurality of bit groups of the LDPC codeword in bit group wise, and divide bits of the other bit groups into sub bit groups and interleave the sub bit groups. In this case, the bits included in the other bit groups, that is, the bits included in the number of groups which correspond to the remainder when the number of bit groups constituting the LDPC codeword is divided by the number of columns are not interleaved in bit group wise, but interleaved by being divided according to the number of columns.

Specifically, the block interleaver 124 may interleave the LDPC codeword by dividing each of the plurality of columns into two parts.

In this case, the block interleaver 124 may divide the plurality of columns into the first part and the second part based on at least one of the number of columns of the block interleaver 124, the number of bit groups of the LDPC codeword, and the number of bits of bit groups.

Here, each of the plurality of bit groups may be formed of 360 bits. In addition, the number of bit groups of the LDPC codeword is determined based on the length of the LDPC codeword and the number of bits included in the bit group. For example, when an LDPC codeword in the length of 16200 is divided such that each bit group has 360 bits, the LDPC codeword is divided into 45 bit groups. Alternatively, when an LDPC codeword in the length of 64800 is divided such that each bit group has 360 bits, the LDPC codeword may be divided into 180 bit groups. Further, the number of columns constituting the block interleaver 124 may be determined according to a modulation method. This will be explained in detail below.

Accordingly, the number of rows constituting each of the first part and the second part may be determined based on the number of columns constituting the block interleaver 124, the number of bit groups constituting the LDPC codeword, and the number of bits constituting each of the plurality of bit groups.

Specifically, in each of the plurality of columns, the first part may be formed of as many rows as the number of bits included in at least one bit group which can be written in each column in bit group wise from among the plurality of bit groups of the LDPC codeword, according to the number of columns constituting the block interleaver 124, the number of bit groups constituting the LDPC codeword, and the number of bits constituting each bit group.

In each of the plurality of columns, the second part may be formed of rows excluding as many rows as the number of bits included in at least some bit groups which can be written in each of the plurality of columns in bit group wise. Specifically, the number rows of the second part may be the same value as a quotient when the number of bits included in all bit groups excluding bit groups corresponding to the first part is divided by the number of columns constituting the block interleaver 124. In other words, the number of rows of the second part may be the same value as a quotient when the number of bits included in the remaining bit groups which are not written in the first part from among bit groups constituting the LDPC codeword is divided by the number of columns.

That is, the block interleaver 124 may divide each of the plurality of columns into the first part including as many rows as the number of bits included in bit groups which can be written in each column in bit group wise, and the second part including the other rows.

Accordingly, the first part may be formed of as many rows as the number of bits included in bit groups, that is, as many rows as an integer multiple of M. However, since the number of codeword bits constituting each bit group may be an aliquot part of M as described above, the first part may be formed of as many rows as an integer multiple of the number of bits constituting each bit group.

In this case, the block interleaver 124 may interleave by writing and reading the LDPC codeword in the first part and the second part in the same method.

Specifically, the block interleaver 124 may interleave by writing the LDPC codeword in the plurality of columns constituting each of the first part and the second part in a column direction, and reading the plurality of columns constituting the first part and the second part in which the LDPC codeword is written in a row direction.

That is, the block interleaver 124 may interleave by writing the bits included in at least some bit groups which can be written in each of the plurality of columns in bit group wise in each of the plurality of columns of the first part serially, dividing the bits included in the other bit groups except the at least some bit groups and writing in each of the plurality of columns of the second part in a column direction, and reading the bits written in each of the plurality of columns constituting each of the first part and the second part in a row direction.

In this case, the block interleaver 124 may interleave by dividing the other bit groups except the at least some bit groups from among the plurality of bit groups based on the number of columns constituting the block interleaver 124.

Specifically, the block interleaver 124 may interleave by dividing the bits included in the other bit groups by the number of a plurality of columns, writing each of the divided bits in each of a plurality of columns constituting the second part in a column direction, and reading the plurality of columns constituting the second part, where the divided bits are written, in a row direction.

That is, the block interleaver 124 may divide the bits included in the other bit groups except the bit groups written in the first part from among the plurality of bit groups of the LDPC codeword, that is, the bits in the number of bit groups which correspond to the remainder when the number of bit groups constituting the LDPC codeword is divided by the number of columns, by the number of columns, and may write the divided bits in each column of the second part serially in a column direction.

For example, it is assumed that the block interleaver 124 is formed of C number of columns each including R₁ number of rows. In addition, it is assumed that the LDPC codeword is formed of N_(group) number of bit groups, the number of bit groups N_(group) is not a multiple of C, and A×C+1=N_(group) (A is an interger greater than 0). In other words, it is assumed that when the number of bit groups constituting the LDPC codeword is divided by the number of columns, the quotient is A and the remainder is 1.

In this case, as shown in FIGS. 10 and 11, the block interleaver 124 may divide each column into a first part including R₁ number of rows and a second part including R₂ number of rows. In this case, R₁ may correspond to the number of bits included in bit groups which can be written in each column in bit group wise, and R₂ may be R₁ subtracted from the number of rows of each column.

That is, in the above-described example, the number of bit groups which can be written in each column in bit group wise is A, and the first part of each column may be formed of as many rows as the number of bits included in A number of bit groups, that is, may be formed of as many rows as A×M number.

In this case, the block interleaver 124 writes the bits included in the bit groups which can be written in each column in bit group wise, that is, A number of bit groups, in the first part of each column in the column direction.

That is, as shown in FIGS. 10 and 11, the block interleaver 124 writes the bits included in each of bit group Y₀, bit group Y₁, . . . , group Y_(A−1) in the 1^(st) to R₁ ^(th) rows of the first part of the 1^(st) column, writes bits included in each of bit group Y_(A), bit group Y_(A+1), . . . , bit group Y_(2A−1) in the 1^(st) to R₁ ^(th) rows of the first part of the 2^(nd) column, . . . , writes bits included in each of bit group Y_(CA−A), bit group Y_(CA−A+1), . . . , bit group Y_(CA−1) in the 1^(st) to R₁ ^(th) rows of the first part of the column C.

As described above, the block interleaver 124 writes the bits included in the bit groups which can be written in each column in bit group wise in the first part of each column.

In other words, in the above exemplary embodiment, the bits included in each of bit group (Y₀), bit group (Y₁), . . . , bit group (Y_(A−1)) may not be divided and all of the bits may be written in the first column, the bits included in each of bit group (Y_(A)), bit group (Y_(A+1)), . . . , bit group (Y_(2A−1)) may not be divided and all of the bits may be written in the second column, . . . , and the bits included in each of bit group (Y_(CA−A)), bit group (Y_(CA−A+1)), . . . , group (Y_(CA−1)) may not be divided and all of the bits may be written in the C column. As such, all bit groups interleaved by the first part are written in the same column of the first part.

Thereafter, the block interleaver 124 divides bits included in the other groups except the bit groups written in the first part of each column from among the plurality of bit groups, and writes the bits in the second part of each column in the column direction. In this case, the block interleaver 124 divides the bits included in the other bit groups except the bit groups written in the first part of each column by the number of columns, so that the same number of bits are written in the second part of each column, and writes the divided bits in the second part of each column in the column direction.

In the above-described example, since A×C+1=N_(group), when the bit groups constituting the LDPC codeword are written in the first part serially, the last bit group Y_(Ngroup−1) of the LDPC codeword is not written in the first part and remains. Accordingly, the block interleaver 124 divides the bits included in the bit group Y_(Ngroup−1) into C number of sub bit groups as shown in FIG. 10, and writes the divided bits (that is, the bits corresponding to the quotient when the bits included in the last group (Y_(Ngroup−1)) are divided by C) in the second part of each column serially.

The bits divided based on the number of columns may be referred to as sub bit groups. In this case, each of the sub bit groups may be written in each column of the second part. That is, the bits included in the bit groups may be divided and may form the sub bit groups.

That is, the block interleaver 124 writes the bits in the 1^(st) to R₂th rows of the second part of the 1^(st) column, writes the bits in the 1^(st) to R₂ ^(th) rows of the second part of the 2^(nd) column, . . . , and writes the bits in the 1^(st) to R₂ ^(th) rows of the second part of the column C. In this case, the block interleaver 124 may write the bits in the second part of each column in the column direction as shown in FIG. 10.

That is, in the second part, the bits constituting the bit group may not be written in the same column and may be written in the plurality of columns. In other words, in the above example, the last bit group (Y_(Ngroup−1)) is formed of M number of bits and thus, the bits included in the last bit group (Y_(Ngroup−1)) may be divided by M/C and written in each column. That is, the bits included in the last bit group (Y_(Ngroup−1)) are divided by M/C, forming M/C number of sub bit groups, and each of the sub bit groups may be written in each column of the second part.

Accordingly, in at least one bit group which is interleaved by the second part, the bits included in the at least one bit group are divided and written in at least two columns constituting the second part.

In the above-described example, the block interleaver 124 writes the bits in the second part in the column direction. However, this is merely an example. That is, the block interleaver 124 may write the bits in the plurality of columns of the second parts in a row direction. In this case, the block interleaver 124 may write the bits in the first part in the same method as described above.

Specifically, referring to FIG. 11, the block interleaver 124 writes the bits from the 1^(st) row of the second part in the 1^(st) column to the 1^(st) row of the second part in the column C, writes the bits from the 2^(nd) row of the second part in the 1^(st) column to the 2^(nd) row of the second part in the column C, . . . , etc., and writes the bits from the R₂ ^(th) row of the second part in the 1^(st) column to the R₂ ^(th) row of the second part in the column C.

On the other hand, the block interleaver 124 reads the bits written in each row of each part serially in the row direction. That is, as shown in FIGS. 10 and 11, the block interleaver 124 reads the bits written in each row of the first part of the plurality of columns serially in the row direction, and reads the bits written in each row of the second part of the plurality of columns serially in the row direction.

Accordingly, the block interleaver 124 may interleave a part of the plurality of bit groups constituting the LDPC codeword in bit group wise, and divide and interleave some of the remaining bit groups. That is, the block interleaver 124 may interleave by writing the LDPC codeword constituting a predetermined number of bit groups from among the plurality of bit groups in the plurality of columns of the first part in bit group wise, dividing the bits of the other bit groups and writing the bits in each of the columns of the second part, and reading the plurality of columns of the first and second parts in the row direction.

As described above, the block interleaver 124 may interleave the plurality of bit groups in the methods described above with reference to FIGS. 9 to 11.

In particular, in the case of FIG. 10, the bits included in the bit group which does not belong to the first part are written in the second part in the column direction and read in the row direction. In view of this, the order of the bits included in the bit group which does not belong to the first part is rearranged. Since the bits included in the bit group which does not belong to the first part are interleaved as described above, Bit Error Rate (BER)/Frame Error Rate (FER) performance can be improved in comparison with a case in which such bits are not interleaved.

However, the bit group which does not belong to the first part may not be interleaved as shown in FIG. 11. That is, since the block interleaver 124 writes and read the bits included in the group which does not belong to the first part in and from the second part in the row direction, the order of the bits included in the group which does not belong to the first part is not changed and the bits are output to the modulator 130 serially. In this case, the bits included in the group which does not belong to the first part may be output serially and mapped onto a modulation symbol.

In FIGS. 10 and 11, the last single bit group of the plurality of bit groups is written in the second part. However, this is merely an example. The number of bit groups written in the second part may vary according to the total number of bit groups of the LDPC codeword, the number of columns and rows, the number of transmission antennas, etc.

The block interleaver 124 may have a configuration as shown in Tables 57 and 58 presented below:

TABLE 57 N_(ldpc) = 64800 16 64 256 1024 4096 QPSK QAM QAM QAM QAM QAM C 2 4 6 8 10 12 R₁ 32400 16200 10800 7920 6480 5400 R₂ 0 0 0 180 0 0

TABLE 58 N_(ldpc) = 16200 QPSK 16 QAM 64 QAM 256 QAM 1024 QAM 4096 QAM C 2 4 6 8 10 12 R₁ 7920 3960 2520 1800 1440 1080 R₂ 180 90 180 225 180 270

Herein, C (or N_(C)) is the number of columns of the block interleaver 124, R₁ is the number of rows constituting the first part in each column, and R₂ is the number of rows constituting the second part in each column.

Referring to Tables 57 and 58, the number of columns has the same value as a modulation order according to a modulation method, and each of a plurality of columns is formed of rows corresponding to the number of bits constituting the LDPC codeword divided by the number of a plurality of columns.

For example, when the length N_(ldpc) of the LDPC codeword is 64800 and the modulation method is QPSK, the block interleaver 124 is formed of 2 columns as the modulation order is 2 in the case of QPSK, and each column is formed of rows as many as R₁+R₂=32400(=64800/2).

Meanwhile, referring to Tables 57 and 58, when the number of bit groups constituting an LDPC codeword is an integer multiple of the number of columns, the block interleaver 124 interleaves without dividing each column. Therefore, R₁ corresponds to the number of rows constituting each column, and R₂ is 0. In addition, when the number of bit groups constituting an LDPC codeword is not an integer multiple of the number of columns, the block interleaver 124 interleaves the groups by dividing each column into the first part formed of R₁ number of rows, and the second part formed of R₂ number of rows.

When the number of columns of the block interleaver 124 is equal to the number of bits constituting a modulation symbol, bits included in a same bit group are mapped onto a single bit of each modulation symbol as shown in Tables 57 and 58.

For example, when N_(ldpc)=64800 and the modulation method is QPSK, the block interleaver 124 may be formed of two (2) columns each including 32400 rows. In this case, a plurality of bit groups are written in the two (2) columns in bit group wise and bits written in the same row in each column are output serially. In this case, since two (2) bits constitute a single modulation symbol in the modulation method of QPSK, bits included in the same bit group, that is, bits output from a single column, may be mapped onto a single bit of each modulation symbol. For example, bits included in a bit group written in the 1^(St) column may be mapped onto the first bit of each modulation symbol.

Referring to Tables 57 and 58, the total number of rows of the block interleaver 124, that is, R₁+R₂, is N_(ldpc)/C.

In addition, the number of rows of the first part, R₁, is an integer multiple of the number of bits included in each group, M (e.g., M=360), and maybe expressed as └N_(group)/C┘×M, and the number of rows of the second part, R₂, may be N_(ldpc)/C−R₁. Herein, └N_(group)/C┘ is the largest integer below N_(group)/C. Since R₁ is an integer multiple of the number of bits included in each group, M, bits may be written in R₁ in bit groups wise.

In addition, when the number of bit groups of the LDPC codeword is not a multiple of the number of columns, it can be seen from Tables 57 and 58 that the block interleaver 124 interleaves by dividing each column into two parts.

Specifically, the length of the LDPC codeword divided by the number of columns is the total number of rows included in the each column. In this case, when the number of bit groups of the LDPC codeword is a multiple of the number of columns, each column is not divided into two parts. However, when the number of bit groups of the LDPC codeword is not a multiple of the number of columns, each column is divided into two parts.

For example, it is assumed that the number of columns of the block interleaver 124 is identical to the number of bits constituting a modulation symbol, and an LDPC codeword is formed of 64800 bits as shown in Table 57. In this case, each bit group of the LDPC codeword is formed of 360 bits, and the LDPC codeword is formed of 64800/360 (=180) bit groups.

When the modulation method is QPSK, the block interleaver 124 may be formed of two (2) columns and each column may have 64800/2 (=32400) rows.

In this case, since the number of bit groups of the LDPC codeword divided by the number of columns is 180/2 (=90), bits can be written in each column in bit group wise without dividing each column into two parts. That is, bits included in 90 bit groups which is the quotient when the number of bit groups constituting the LDPC codeword is divided by the number of columns, that is, 90×360 (=32400) bits can be written in each column.

However, when the modulation method is 256-QAM, the block interleaver 124 may be formed of eight (8) columns and each column may have 64800/8(=8100) rows.

In this case, since the number of bit groups of the LDPC codeword divided by the number of columns is 180/8=22.5, the number of bit groups constituting the LDPC codeword is not an integer multiple of the number of columns. Accordingly, the block interleaver 124 divides each of the eight (8) columns into two parts to perform interleaving in bit group wise.

In this case, since the bits should be written in the first part of each column in bit group wise, the number of bit groups which can be written in the first part of each column in bit group wise is 22 which is the quotient when the number of bit groups constituting the LDPC codeword is divided by the number of columns, and accordingly, the first part of each column has 22×360 (=7920) rows. Accordingly, 7920 bits included in 22 bit groups may be written in the first part of each column.

The second part of each column has rows which are the rows of the first part subtracted from the total rows of each column. Accordingly, the second part of each column includes 8100-7920 (=180) rows.

In this case, the bits included in the other bit groups which have not been written in the first part are divided and written in the second part of each column.

Specifically, since 22×8 (=176) bit groups are written in the first part, the number of bit groups to be written in the second part is 180-176 (=4) (for example, bit group Y₁₇₆, bit group Y₁₇₇, bit group Y₁₇₈, and bit group Y₁₇₉ from among bit group Y₀, bit group Y₁, bit group Y₂, . . . , bit group Y₁₇₈, and bit group Y₁₇₉ constituting the LDPC codeword).

Accordingly, the block interleaver 124 may write the four (4) bit groups which have not been written in the first part and remains from among the groups constituting the LDPC codeword in the second part of each column serially.

That is, the block interleaver 124 may write 180 bits of the 360 bits included in the bit group Y₁₇₆ in the 1^(st) row to the 180^(th) row of the second part of the 1^(st) column in the column direction, and may write the other 180 bits in the 1^(st) row to the 180^(th) row of the second part of the 2^(nd) column in the column direction. In addition, the block interleaver 124 may write 180 bits of the 360 bits included in the bit group Y₁₇₇ in the 1^(st) row to the 180^(th) row of the second part of the 3^(rd) column in the column direction, and may write the other 180 bits in the 1^(st) row to the 180^(th) row of the second part of the 4^(th) column in the column direction. In addition, the block interleaver 124 may write 180 bits of the 360 bits included in the bit group Y₁₇₈ in the 1^(st) row to the 180^(th) row of the second part of the 5^(th) column in the column direction, and may write the other 180 bits in the 1^(st) row to the 180^(th) row of the second part of the 6^(th) column in the column direction. In addition, the block interleaver 124 may write 180 bits of the 360 bits included in the bit group Y₁₇₉ in the 1^(st) row to the 180^(th) row of the second part of the 7^(th) column in the column direction, and may write the other 180 bits in the 1^(st) row to the 180^(th) row of the second part of the 8^(th) column in the column direction.

Accordingly, the bits included in the bit group which has not been written in the first part and remains are not written in the same column in the second part and may be divided and written in the plurality of columns.

Hereinafter, the block interleaver of FIG. 5 according to an exemplary embodiment will be explained in detail with reference to FIG. 12.

In a group-interleaved LDPC codeword (v₀, v₁, . . . , ν_(N) _(ldpc) ⁻¹), is continuously arranged like V={Y₀, Y₁, . . . Y_(N) _(group) ⁻¹}.

The LDPC codeword after group interleaving may be interleaved by the block interleaver 124 as shown in FIG. 12. In this case, the block interleaver 124 divide a plurality of columns into the first part (Part 1) and the second part (Part 2) based on the number of columns of the block interleaver 124 and the number of bits of bit groups. In this case, in the first part, the bits constituting the bit groups may be written in the same column, and in the second part, the bits constituting the bit groups may be written in a plurality of columns (i.e. the bits constituting the bit groups may be written in at least two columns).

Specifically, input bits v_(i) are written serially from the first part to the second part column wise, and then read out serially from the first part to the second part row wise. That is, the data bits ν_(i) are written serially into the block interleaver column-wise starting in the first aprt and continuing column-wise finishing in the second part, and then read out serially row-wise from the first part and then row-wise from the second part. Accordingly, the bit included in the same bit group in the first part may be mapped onto a single bit of each modulation symbol.

In this case, the number of columns and the number of rows of the first part and the second part of the block interleaver 124 vary according to a modulation format and a length of the LDPC codeword as in Table 30 presented below. That is, the first part and the second part block interleaving configurations for each modulation format and code length are specified in Table 59 presented below. Herein, the number of columns of the block interleaver 124 may be equal to the number of bits constituting a modulation symbol. In addition, a sum of the number of rows of the first part, N_(r1) and the number of rows of the second part, N_(r2), is equal to N_(ldpc)/N_(C) (herein, N_(C) is the number of columns). In addition, since N_(r1)(=└N_(group)/N_(c)┘×360) is a multiple of 360, a multiple of bit groups may be written in the first part.

TABLE 59 Rows in Part 1 N_(r1) Rows in Part 2 N_(r2) N_(ldpc) = N_(ldpc) = N_(ldpc) = N_(ldpc) = Columns Modulation 64800 16200 64800 16200 N_(C) QPSK 32400 7920 0 180 2  16-QAM 16200 3960 0 90 4  64-QAM 10800 2520 0 180 6  256-QAM 7920 1800 180 225 8 1024-QAM 6480 1440 0 180 10 4096-QAM 5400 1080 0 270 12

Hereinafter, an operation of the block interleaver 124 will be explained in detail.

Specifically, as shown in FIG. 12, the input bit v_(i) (0≤i<N_(C)×N_(r1)) is written in r_(i) row of c_(i) column of the first part of the block interleaver 124. Herein, c_(i) and r_(i) are

$c_{i} = \left\lfloor \frac{i}{N_{r\; 1}} \right\rfloor$ and r_(i)=(i mod N_(r1)), respectively.

In addition, the input bit v_(i) (N_(C)×N_(r1)≤i<N_(ldpc)) is written in an r_(i) row of c_(i) column of the second part of the block interleaver 124. Herein, c_(i) and r_(i) satisfy

${c_{i} = {{\left\lfloor \frac{\left( {i - {N_{C} \times N_{r\; 1}}} \right)}{N_{r\; 2}} \right\rfloor\mspace{14mu}{and}\mspace{14mu} r_{i}} = {N_{r\; 1} + \left\{ {\left( {i - {N_{C} \times N_{r\; 1}}} \right)\mspace{11mu}{mod}\; N_{r\; 2}} \right\}}}},$ mod N_(r2), respectively.

An output bit q_(j)(0≤j<N_(ldpc)) is read from c_(j) column of r_(j) row. Herein, r_(j) and c_(j) satisfy

$r_{j} = \left\lfloor \frac{j}{N_{c}} \right\rfloor$ and c_(j)=(j mod N_(C)), respectively.

For example, when the length N_(ldpc) of an LDPC codeword is 64800 and the modulation method is 256-QAM, the order of bits output from the block interleaver 124 may be (q₀, q₁, q₂, . . . , q₆₃₃₅₇, q₆₃₃₅₈, q₆₃₃₅₉, q₆₃₃₆₀, q₆₃₃₆₁, . . . , q₆₄₇₉₉)=(v₀, v₇₉₂₀, v₁₅₈₄₀, . . . , v₄₇₅₁₉, v₅₅₄₃₉, v₆₃₃₅₉, v₆₃₃₆₀, v₆₃₅₄₀, . . . , v₆₄₇₉₉) Herein, the indexes of the right side of the foregoing equation may be specifically expressed for the eight (8) columns as 0, 7920, 15840, 23760, 31680, 39600, 47520, 55440, 1, 7921, 15841, 23761, 31681, 39601, 47521, 55441, . . . , 7919, 15839, 23759, 31679, 39599, 47519, 55439, 63359, 63360, 63540, 63720, 63900, 64080, 64260, 64440, 64620, . . . , 63539, 63719, 63899, 64079, 64259, 64439, 64619, 64799.

Hereinafter, the interleaving operation of the block interleaver 124 will be explained in detail.

The block interleaver 124 may interleave by writing a plurality of bit groups in each column in bit group wise in a column direction, and reading each row of the plurality of columns in which the plurality of bit groups are written in bit group wise in a row direction.

In this case, the number of columns constituting the block interleaver 124 may vary according to a modulation method, and the number of rows may be the length of the LDPC codeword/the number of columns. For example, when the modulation method is QPSK, the block interleaver 124 may be formed of 2 columns. In this case, when the length N_(ldpc) of the LDPC codeword is 16200, the number of rows is 8100 (=16200/2), and, when the length N_(ldpc) of the LDPC codeword is 64800, the number of rows is 32400 (=64800/2).

Hereinafter, the method for interleaving the plurality of bit groups in bit group wise by the block interleaver 124 will be explained in detail.

When the number of bit groups constituting the LDPC codeword is an integer multiple of the number of columns, the block interleaver 124 may interleave by writing the bit groups as many as the number of bit groups divided by the number of columns in each column serially in bit group wise.

For example, when the modulation method is QPSK and the length N_(ldpc) of the LDPC codeword is 64800, the block interleaver 124 may be formed of two (2) columns each including 32400 rows. In this case, since the LDPC codeword is divided into (64800/360=180) number of bit groups when the length N_(ldpc) of the LDPC codeword is 64800, the number of bit groups (=180) of the LDPC codeword may be an integer multiple of the number of columns (=2) when the modulation method is QPSK.

In this case, as shown in FIG. 13, the block interleaver 124 writes the bits included in each of the bit group Y₀, bit group Y₁ . . . , bit group Y₈₉ in the 1^(st) row to 32400^(th) row of the first column, and writes the bits included in each of the bit group Y₉₀, the bit group Y₉₁, . . . , the bit group Y₁₇₉ in the 1^(st) row to 32400^(th) row of the second column. In addition, the block interleaver 124 may read the bits written in each row of the two columns serially in the row direction.

However, when the number of bit groups constituting the LDPC codeword is not an integer multiple of the number of columns, the block interleaver 124 may interleave by dividing each column into N number of parts (N is an integer greater than or equal to 2).

Specifically, the block interleaver 124 may divide each column into a part including as many rows as the number of bits included in the bit group which can be written in each column in bit group wise, and a part including the other rows, and may interleave by using the divided parts.

In this case, the block interleaver 124 may write at least some bit groups which can be written in each of the plurality of columns in bit group wise from among the plurality of bit groups in each of the plurality of columns serially, and then divides the bits included in the other bit groups into sub bit groups and writes the bits in the other area remaining in each of the plurality of columns after the at least some bit groups are written in bit group wise. That is, the block interleaver 124 may write the bits included in at least some bit groups which are writable in the first part of each column in bit group wise, and may divide the bits included in the other bit groups and writhe the bits in the second part of each column.

For example, when the modulation method is QPSK and the length N_(ldpc) of the LDPC codeword is 16200, the block interleaver 124 may be formed of two (2) columns each including 8100 rows. In this case, since the LDPC codeword is divided into (16200/360=45) number of bit groups when the length N_(ldpc) of the LDPC codeword is 16200, the number of bit groups (=45) of the LDPC codeword is not an integer multiple of the number of columns (=2) when the modulation method is QPSK. That is, a remainder exists.

In this case, the block interleaver 124 may divide each column into the first part including 7920 rows and the second part including 180 rows as shown in FIGS. 14 and 15.

The block interleaver 124 writes the bits included in the bit groups which can be written in each column in bit group wise in the first part of each column in the column direction.

That is, as shown in FIGS. 14 and 15, the block interleaver 124 writes the bits included in each of the bit group Y₀, bit group Y₁ . . . , bit group Y₂₁ in the 1^(st) row to 7920^(th) row of the first part of the first column, and writes the bits included in each of the bit group Y₂₂, the bit group Y₂₃, . . . , the bit group Y₄₃ in the 1^(st) row to 7920^(th) row of the first part of the second column.

As described above, the block interleaver 124 writes the bits included in the bit groups which can be written in each column in bit group wise in the first part of each column in bit group wise.

Thereafter, the block interleaver 124 divides the bits included in the other bit groups except for the bit groups written in the first part of each column from among the plurality of bit groups, and writes the bits in the second part of each column in the column direction. In this case, the block interleaver 124 may divide the bits included in the other bit groups except for the bit groups written in the first part of each column by the number of columns, such that the same number of bits are written in the second part of each column, and writes the divided bits in each column of the second part in the column direction.

For example, when the bit group Y₄₄, which is the last bit group of the LDPC codeword, remains as shown in FIG. 14, the block interleaver 124 divides the bits included in the bit group Y₄₄ by 2, and writes the divided bits in the second part of each column serially.

That is, the block interleaver 124 may write the bits in the 1^(st) row to 180^(th) row of the second part of the first column, and writes the bits in the 1^(st) row to 180^(th) row of the second part of the second column. In this case, the block interleaver 124 may write the bits in the second part of each column in the column direction as shown in FIG. 14. That is, the bits constituting the bit group are not written in the same column in the second part and are written in the plurality of columns.

In the above-described example, the block interleaver 124 writes the bits in the second part in the column direction. However, this is merely an example. That is, the block interleaver 124 may write the bits in the plurality of columns of the second part in the row direction. However, the block interleaver 124 may write the bits in the first part in the same method as described above.

Specifically, referring to FIG. 15, the block interleaver 124 may write the bits in the 1^(st) row of the second part of the first column to the 1^(st) row of the second part of the second column, writes the bits in the 2^(nd) row of the second part of the first column to the 2^(nd) row of the second part of the second column, . . . , writes the bits in the 180^(th) row of the second part of the first column to the 180^(th) row of the second part of the second column.

The block interleaver 124 reads the bits written in each row of each part serially in the row direction. That is, as shown in FIGS. 14 and 15, the block interleaver 124 may read the bits written in each row of the first part of the plurality of columns serially in the row direction, and may read the bits written in each row of the second part of the plurality of columns serially in the row direction.

As described above, the block interleaver 124 may interleave the plurality of bit groups in the method described above with reference to FIGS. 13 to 15.

The modulator 130 maps the interleaved LDPC codeword onto a modulation symbol. Specifically, the modulator 130 may demultiplex the interleaved LDPC codeword, modulate the demultiplexed LDPC codeword, and map the LDPC codeword onto a constellation.

In this case, the modulator 130 may generate a modulation symbol using the bits included in each of a plurality of bit groups.

In other words, as described above, the bits included in different bit groups are written in each column of the block interleaver 124, and the block interleaver 124 reads the bits written in each column in the row direction. In this case, the modulator 130 generates a modulation symbol by mapping the bits read in each column onto each bit of the modulation symbol. Accordingly, each bit of the modulation symbol belongs to a different group.

For example, it is assumed that the modulation symbol consists of C number of bits. In this case, the bits which are read from each row of C number of columns of the block interleaver 124 may be mapped onto each bit of the modulation symbol and thus, each bit of the modulation symbol consisting of C number of bits belong to C number of different groups.

Hereinbelow, the above feature will be described in greater detail.

First, the modulator 130 demultiplexes the interleaved LDPC codeword. To achieve this, the modulator 130 may include a demultiplexer (not shown) to demultiplex the interleaved LDPC codeword.

The demultiplexer (not shown) demultiplexes the interleaved LDPC codeword. Specifically, the demultiplexer (not shown) performs serial-to-parallel conversion with respect to the interleaved LDPC codeword, and demultiplexes the interleaved LDPC codeword into a cell having a predetermined number of bits (or a data cell).

For example, as shown in FIG. 16, the demultiplexer (not shown) receives an LDPC codeword Q=(q₀, q₁, q₂, . . . ) output from the interleaver 120, outputs the received LDPC codeword bits to a plurality of substreams serially, converts the input LDPC codeword bits into cells, and outputs the cells.

In this case, bits having a same index in each of the plurality of substreams may constitute a same cell. Accordingly, the cells may be configured like (y_(0,0), y_(1,0), . . . , y_(η MOD−1,0))=(q₀, q₁, q_(η MOD−1)), (y_(0,1), y_(1,1), . . . , y_(η MOD−1,1))=(q_(η MOD), q_(η MOD+1), . . . , q_(2×η MOD−1)), . . . .

Herein, the number of substreams, N_(substreams), may be equal to the number of bits constituting a modulation symbol, η_(MOD). Accordingly, the number of bits constituting each cell may be equal to the number of bits constituting a modulation symbol (that is, a modulation order).

For example, when the modulation method is QPSK, the number of bits constituting the modulation symbol, η_(MOD), is 2, and thus, the number of substreams, N_(substreams), is 2, and the cells may be configured like (y_(0,0), y_(1,0))=(q₀, q₁), (y_(0,1), y_(1,1))=(q₂,q₃), (y_(0,2), y_(1,2))=(q₄, q₅), . . . .

The modulator 130 may map the demultiplexed LDPC codeword onto modulation symbols.

Specifically, the modulator 130 may modulate bits (that is, cells) output from the demultiplexer (not shown) in various modulation methods. For example, when the modulation method is QPSK, 16-QAM, 64-QAM, 256-QAM, 1024-QAM, and 4096-QAM, the number of bits constituting a modulation symbol, η_(MOD) (that is, the modulation order), may be 2, 4, 6, 8, 10 and 12, respectively.

In this case, since each cell output from the demultiplexer (not shown) is formed of as many bits as the number of bits constituting a modulation symbol, the modulator 130 may generate a modulation symbol by mapping each cell output from the demultiplexer (not shown) onto a constellation point serially. Herein, a modulation symbol corresponds to a constellation point on a constellation.

However, the above-described demultiplexer (not shown) may be omitted according to circumstances. In this case, the modulator 130 may generate modulation symbols by grouping a predetermined number of bits from interleaved bits serially and mapping the predetermined number of bits onto constellation points. In this case, the modulator 130 may generate modulation symbols by mapping η_(MOD) number of bits onto the constellation points serially according to a modulation method.

When an LDPC codeword is generated based on the parity check matrix defined as in Tables 4 to 21 and Tables 23 to 31, a plurality of bit groups of the LDPC codeword are interleaved by using interleaving parameters defined as in Tables 32 to 56 for the following reasons.

In general, when modulation is performed by using QPSK, encoding/decoding performance depends on how LDPC codeword bits are mapped onto two bits of a QPSK symbol.

In particular, when two parity bits are connected to a single check node in a parity check matrix, good performance can be guaranteed by mapping the two parity bits onto a single QPSK symbol. In addition, good performance can be guaranteed by mapping two parity bits connected to a single check node in the parity check matrix onto a single QPSK symbol. In addition, when there are a plurality of parity bits each connected to a single check node in a parity check matrix, good performance can be guaranteed by selecting two check nodes and mapping two parity bits connected to the two check nodes onto a single QPSK symbol.

Accordingly, after the LDPC codeword bits generated based on the parity check matrix defined as in Tables 4 to 21 and Tables 23 to 31 are group-interleaved based on Equation 21 and Tables 32 to 56, when the interleaved LDPC codeword bits are modulated by QPSK, two parity bits connected to a single check node may be mapped onto a same QPSK symbol or two parity bits connected to the selected two check nodes may be mapped onto a same QPSK symbol. Accordingly, encoding/decoding performance can be improved and the transmitting apparatus is robust to a burst error.

Specifically, since the order of bit groups to be written/read in the plurality of columns of the block interleaver 124 is determined according to the interleaving in bit group wise in the group interleaver 122, bits to be mapped onto a modulation symbol may be determined according to the interleaving in bit group wise in the group interleaver 122.

Accordingly, the group interleaver 122 may interleave the LDPC codeword bits in bit group wise such that bits belonging to a predetermined number of continuous bit groups, that is, bits connected to a predetermined number of same check nodes, are mapped onto a same QPSK symbol, by considering reliability of bits mapped onto a modulation symbol and performance of the codeword bits of the LDPC codeword. To achieve this, the group interleaver 122 may interleave the LDPC codeword bits in bit group wise based on Equation 21 and Tables 32 to 56.

Hereinafter, a method for designing the group interleaver 122 according to an exemplary embodiment will be explained. For the convenience of explanation, a method for defining π(j) with reference to Table 33 from among Tables 32 to 56 by way of an example will be explained.

In the case of the QPSK modulation method, the block interleaver 124 is formed of two columns, and two bits read and output from a same row of two columns configure a same QPSK symbol. Accordingly, bits of continuous bit groups from among the plurality of bit groups of the LDPC codeword should be written in a same row in each of the two columns of the block interleaver 124 to be mapped onto a same QPSK symbol.

That is, in order to map two parity bits connected to a single check node in the parity check matrix onto a same QPSK modulation symbol, bits belonging to two continuous bit groups to which the two parity bits belong should be written in a same row in each of the two columns of the block interleaver 124.

When bits included in two continuous bit groups from the 25^(th) bit group to the 44^(th) bit group from among 45 bit groups constituting an LDPC codeword (that is, the 0^(th) to 44^(th) bit groups) should be mapped onto a same QPSK symbol for the purpose of improving encoding/decoding performance, and it is assumed that the 26^(th) bit group, 28^(th) bit group, . . . , 42^(nd) bit group, and 44^(th) bit groups are written in the 4321^(st) row to the 7920^(th) row of the first part of the first column of the block interleaver 124 as shown in (a) of FIG. 17, the 25^(th) bit group, 27^(th) bit group, . . . , 41^(st) bit group, and 43^(rd) bit group should be written in the 4321^(st) row to the 7920^(th) row of the first part of the second column.

In this case, encoding/decoding performance depends on which bit groups are mapped onto a same modulation symbol (in the above-described example, two continuous bit groups from the 25^(th) bit group to the 44^(th) bit group are mapped onto the same modulation symbol). Therefore, the other bit groups may be randomly written in the block interleaver 124.

That is, in the above-described example, the 0^(th) bit group to the 24^(th) bit group may be randomly written in the other rows of the first part and the second part which remain after the 25^(th) bit group to the 44^(th) bit group are written in the block interleaver 124. For example, as shown in (a) of FIG. 17, the 3^(rd) bit group, 22^(nd) bit group, 7^(th) bit group, . . . , 2^(nd) bit group, 23^(rd) bit group, 11^(th) bit group, 0^(th) bit group, 13^(th) bit group, . . . , 12^(th) bit group, and 16^(th) bit group may be written in the other rows of the first part, and the 8^(th) bit group may be written in the second part.

However, when the LDPC codeword bits are written in each column of the block interleaver 124 in bit group wise as shown in (a) of FIG. 17, the bits included in the 25^(th) bit group to the 44^(th) bit group are mapped onto continuous QPSK symbols, and thus, are vulnerable to a bust error.

Accordingly, in order not to map the bits included in the 25^(th) bit group to the 44^(th) bit group onto continuous QPSK symbols, the rows of the block interleaver 124 may be randomly interleaved (row-wise random interleaving) as shown in (a) of FIG. 17 and the order of the bit groups to be written in the block interleaver 124 may be changed as shown in (b) of FIG. 17.

As a result, when the group interleaver 122 interleaves a plurality of bit groups of an LDPC codeword in the order shown in Table 33, the plurality of bit groups of the LDPC codeword may be written in the block interleaver 124 in the order shown in (b) of FIG. 17, and accordingly, parity bits included in two continuous bit groups may be mapped onto a same QPSK symbol.

That is, when the encoder 110 performs LDPC-encoding in a code rate of 7/15 based on a parity check matrix including an information word submatrix defined by the Table 6 and a parity submatrix having a dual diagonal configuration, and the plurality of bit groups of the LDPC codeword are interleaved by the group interleaver 122 based on π(j) defined by Table 33, the plurality of bit groups of the LDPC codeword may be written in the block interleaver 124 as shown in (b) of FIG. 17, and thus, bits included in two continuous bit groups of 20 bit groups may be mapped onto a same modulation symbol.

In (a) and (b) of FIG. 17, bits included in two continuous bit groups of the 20 bit groups from the 25^(th) bit group to the 44^(th) bit group are mapped onto a same modulation symbol. However, this is merely an example. The number of continuous bit groups to be mapped onto a same modulation symbol may vary according to a parity check matrix and a code rate. That is, when LDPC encoding is performed with a parity check matrix having a different configuration and at a different code rate, the number of continuous bit groups to be mapped onto a same modulation symbol may be changed.

Hereinafter, a method for defining π(j) with reference to Table 36 according to another exemplary embodiment will be explained.

In the case of the QPSK modulation method, the block interleaver 124 is formed of two columns, and two bits read and output from a same row of two columns configure a same QPSK symbol. Accordingly, bits of continuous bit groups from among a plurality of bit groups of an LDPC codeword should be written in a same row in each of two columns of the block interleaver 124 to be mapped onto a same QPSK symbol.

That is, in order to map two parity bits connected to a single check node in a parity check matrix onto a same QPSK modulation symbol, bits belonging to two continuous bit groups to which the two parity bits belong should be written in a same row in each of two columns of the block interleaver 124.

When bits included in two continuous bit groups from the 39^(th) bit group to the 44^(th) bit group from among 45 bit groups constituting an LDPC codeword (that is, the 0^(th) to 44^(th) bit groups) should be mapped onto a same QPSK symbol for the purpose of improving encoding/decoding performance, and it is assumed that the 40^(th) bit group, 42^(nd) bit group, and 44^(th) bit groups are written in the 6841^(st) row to the 7920^(th) row of the first part of the first column of the block interleaver 124 as shown in (a) of FIG. 18, the 39^(th) bit group, 41^(st) bit group, and 43^(rd) bit group should be written in the 6841^(st) row to the 7920^(th) row of the first part of the second column.

In this case, encoding/decoding performance depends on which bit groups are mapped onto a same modulation symbol (in the above-described example, two continuous bit groups from the 39^(th) bit group to the 44^(th) bit group are mapped onto a same modulation symbol). Therefore, the other bit groups may be randomly written in the block interleaver 124.

That is, in the above-described example, the 0^(th) bit group to the 38^(th) bit group may be randomly written in the other rows of the first part and the second part which remain after the 39^(th) bit group to the 44^(th) bit group are written in the block interleaver 124. For example, as shown in (a) of FIG. 18, the 13^(th) bit group, 10^(th) bit group, 0^(th) bit group, . . . , 36^(th) bit group, 38^(th) bit group, 6^(th) bit group, 7^(th) bit group, 17^(th) bit group, . . . , 35^(th) bit group, and 37^(th) bit group may be written in the other rows of the first part, and the 1^(st) bit group may be written in the second part.

However, when LDPC codeword bits are written in each column of the block interleaver 124 in bit group wise as shown in (a) of FIG. 18, bits included in the 39^(th) bit group to the 44^(th) bit group are mapped onto continuous QPSK symbols, and thus, are vulnerable to a bust error.

Accordingly, in order not to map bits included in the 39^(th) bit group to the 44^(th) bit group onto continuous QPSK symbols, the rows of the block interleaver 124 may be randomly interleaved (row-wise random interleaving) as shown in (a) of FIG. 18 and the order of the bit groups to be written in the block interleaver 124 may be changed as shown in (b) of FIG. 18.

As a result, when the group interleaver 122 interleaves a plurality of bit groups of an LDPC codeword in the order shown in Table 36, the plurality of bit groups of the LDPC codeword may be written in the block interleaver 124 in the order shown in (b) of FIG. 18, and accordingly, parity bits included in two continuous bit groups may be mapped onto a same QPSK symbol.

That is, when the encoder 110 performs LDPC-encoding in a code rate of 13/15 based on a parity check matrix including an information word submatrix defined by Table 12 and a parity submatrix having a dual diagonal configuration, and the plurality of bit groups of the LDPC codeword are interleaved by the group interleaver 122 based on π(j) defined by Table 36, the plurality of bit groups of the LDPC codeword may be written in the block interleaver 124 as shown in (b) of FIG. 18, and thus, bits included in two continuous bit groups of 6 bit groups may be mapped onto a same modulation symbol.

In (a) and (b) of FIG. 18, bits included in two continuous bit groups of the 6 bit groups from the 39^(th) bit group to the 44^(th) bit group are mapped onto a same modulation symbol. However, this is merely an example. The number of continuous bit groups to be mapped onto a same modulation symbol may vary according to a parity check matrix and a code rate. That is, when LDPC encoding is performed with a parity check matrix having a different configuration and at a different code rate, the number of continuous bit groups to be mapped onto a same modulation symbol may be changed.

In addition, since performance is greatly affected by which continuous bit groups are mapped onto a same modulation symbol, the other bit groups except for the continuous bit groups mapped onto the same modulation symbol may be randomly written in the plurality of columns as shown in (a) and (b) of FIG. 17 or (a) and (b) of FIG. 18.

Accordingly, as long as a same bit group is mapped onto a same modulation symbol, interleaving may be regarded as being performed in the same method as the group interleaver presented in the present disclosure.

TABLE 60 A A_perm B_perm C_perm D_perm E_perm j-th (j)-th (j)-th (j)-th (j)-th (j)-th (j)-th block of block of block of block of block of block of block of Group- Group- Group- Group- Group- Group- Group- wise wise wise wise wise wise wise Inter- Inter- Inter- Inter- Inter- Inter- Inter- leaver leaver leaver leaver leaver leaver leaver output input input input input input input 0 3 4 0 2 17 23 1 22 22 2 1 16 22 2 7 23 19 3 18 24 3 18 44 44 44 44 44 4 6 34 34 34 34 34 5 1 1 10 17 0 9 6 4 3 11 15 3 7 7 14 2 9 16 2 5 8 5 32 32 32 32 32 9 15 42 42 42 42 42 10 2 6 20 6 12 18 11 23 15 23 7 11 19 12 26 30 30 30 30 30 13 28 40 40 40 40 40 14 30 18 16 10 21 3 15 32 5 15 11 22 1 16 34 28 28 28 28 28 17 36 38 38 38 38 38 18 38 7 6 21 8 14 19 40 14 5 22 7 13 20 42 26 26 26 26 26 21 44 36 36 36 36 36 22 11 9 13 18 5 8 23 0 0 14 24 23 10 24 13 16 12 19 4 6 25 10 43 43 43 43 43 26 21 33 33 33 33 33 27 17 17 1 0 1 16 28 9 11 4 20 6 15 29 19 12 3 5 24 17 30 24 31 31 31 31 31 31 20 41 41 41 41 41 32 12 21 18 4 19 4 33 16 20 17 9 20 2 34 25 29 29 29 29 29 35 27 39 39 39 39 39 36 29 10 8 8 10 0 37 31 24 7 23 9 21 38 33 27 27 27 27 27 39 35 37 37 37 37 37 40 37 13 24 12 14 20 41 39 19 22 13 15 12 42 41 25 25 25 25 25 43 43 35 35 35 35 35 44 8 8 21 14 13 11

For example, in Table 60, A and A_perm indicate π(j) after/before row-wise random interleaving is performed, and B_perm, C_perm, D_perm, and E_perm indicate π(j) when row-wise random interleaving is performed after the other bit groups except for continuous bit groups are randomly written in the plurality of columns in different methods. Referring to Table 60, in B_perm, C_perm, D_perm, and E_perm, the same group as in A_perm is mapped onto a same modulation symbol. Accordingly, it can be seen that a same interleaving method as in A_perm is used for B_perm, C_perm, D_perm, and E_perm.

In the above-described example, an interleaving pattern in the case of a parity check matrix having the configuration of FIG. 2 has been described. Hereinafter, a method for designing an interleaving pattern when a parity check matrix has the configuration of FIG. 4 will be explained with reference to Table 32.

When there are bit groups formed of parity bits connected to a single check node from among a plurality of bit groups of the LDPC codeword, bits included in two bit groups selected from the corresponding bit groups should be written in a same row of two columns of the block interleaver 124.

It is assumed that the 18^(th) bit group to the 44^(th) bit group from among the 45 bit groups (that is, 0^(th) to 44^(th) bit groups) of an LDPC codeword are bit groups formed of parity bits connected to a single check node connected to a single parity bit, and two bits are selected from the corresponding bit groups and 2880 (=8×360) QPSK symbols in total should be generated.

In this case, as shown in (a) of FIG. 19, 8 bit groups randomly selected from among the 18^(th) bit group to the 44^(th) bit group should be written in the 5041^(st) row to the 7920^(th) row of the first part of the first column, and the other 8 bit groups randomly selected should be written in the 5041^(st) row to the 7920^(th) row of the first part of the second column.

Since encoding/decoding performance depends on how many QPSK symbols are formed of parity bits connected to a single check node connected to a single parity bit, the other bit groups may be randomly written in the block interleaver 124.

Accordingly, the 29 bit groups which are not selected in the above-described example may be randomly written in the other rows of the first part, and the second part which remain after the selected groups are written in the block interleaver 124. For example, as shown in (a) of FIG. 19, the 0^(th) bit group, 17^(th) bit group, 38^(th) bit group, . . . , 37^(th) bit group, 5^(th) bit group, and 3^(rd) bit group may be written in the other rows of the first part, and the 8^(th) bit group may be written in the second part.

However, when LDPC codeword bits are written in each column of the block interleaver 124 in bit group wise as shown in (a) of FIG. 19, a bust error may be intensively generated only in the parity bit, and thus, may undermine encoding/decoding performance of the LDPC code. Accordingly, the rows of the block interleaver 124 may be randomly interleaved as shown in (a) of FIG. 19, and the order of the bit groups to be written in the block interleaver 124 may be changed as shown in (b) of FIG. 19, so that a bust error does not affect only the parity bit if any.

As a result, when the group interleaver 122 interleaves a plurality of bit groups of an LDPC codeword in the order of Table 32, the plurality of bit groups of the LDPC codeword may be written in the block interleaver 124 in the order shown in (b) of FIG. 19, and accordingly, a QPSK symbol formed of only parity bits connected to a check node connected to a single parity bit may be generated.

That is, when the encoder 110 performs LDPC encoding based on the parity check matrix defined in Table 26 at a code rate of 5/15, and the group interleaver 122 interleaves a plurality of bit groups of an LDPC codeword based on π(j) defined by Table 32, the plurality of bit groups of the LDPC codeword may be written in the block interleaver 124 as shown in (b) of FIG. 19, and thus, bits included in two continuous bit groups of 16 bit groups may be mapped onto a same modulation symbol.

In (a) and (b) of FIG. 19, only the 16 bit groups are randomly selected from the 18^(th) bit group to the 44^(th) bit group and a modulation symbol formed of only bits included in selected bit groups is generated. However, this is merely an example. The number of bit groups, corresponding to parity bits connected to a check node connected to a single parity bit, which are mapped onto a same modulation symbol, may be changed according to a parity check matrix and a code rate.

The transmitting apparatus 100 may transmit a modulation symbol to a receiving apparatus 1300. For example, the modulator 130 may map the modulation symbol onto an Orthogonal Frequency Division Multiplexing (OFDM) frame using OFDM, and may transmit the modulation symbol mapped onto the OFDM frame to the receiving apparatus 1300 through an allocated channel.

FIG. 20 is a block diagram to illustrate a configuration of a receiving apparatus according to an exemplary embodiment. Referring to FIG. 20, the receiving apparatus 1500 includes a demodulator 1510, a multiplexer 1520, a deinterleaver 1530 and a decoder 1540.

The demodulator 1510 receives and demodulates a signal transmitted from the transmitting apparatus 100. Specifically, the demodulator 1510 generates a value corresponding to an LDPC codeword by demodulating the received signal, and outputs the value to the multiplexer 1520. In this case, the demodulator 1510 may use a demodulation method corresponding to a modulation method used in the transmitting apparatus 100. To do so, the transmitting apparatus 100 may transmit information regarding the modulation method to the receiving apparatus 1500, or the transmitting apparatus 100 may perform modulation using a pre-defined modulation method between the transmitting apparatus 100 and the receiving apparatus 1500.

The value corresponding to the LDPC codeword may be expressed as a channel value for the received signal. There are various methods for determining the channel value, and for example, a method for determining a Log Likelihood Ratio (LLR) value may be the method for determining the channel value.

The LLR value is a log value for a ratio of the probability that a bit transmitted from the transmitting apparatus 100 is 0 and the probability that the bit is 1. In addition, the LLR value may be a bit value which is determined by a hard decision, or may be a representative value which is determined according to a section to which the probability that the bit transmitted from the transmitting apparatus 100 is 0 or 1 belongs.

The multiplexer 1520 multiplexes the output value of the demodulator 1510 and outputs the value to the deinterleaver 1530.

Specifically, the multiplexer 1520 is an element corresponding to a demultiplexer (not shown) provided in the transmitting apparatus 100, and performs an operation corresponding to the demultiplexer (not shown). That is, the multiplexer 1520 performs an inverse operation of the operation of the demultiplexer (not shown), and performs cell-to-bit conversion with respect to the output value of the demodulator 1510 and outputs the LLR value in the unit of bit. However, when the demultiplexer (not shown) is omitted from the transmitting apparatus 100, the multiplexer 1520 may be omitted from the receiving apparatus 1500.

The information regarding whether the demultiplexing operation is performed or not may be provided by the transmitting apparatus 100, or may be pre-defined between the transmitting apparatus 100 and the receiving apparatus 1500.

The deinterleaver 1530 deinterleaves the output value of the multiplexer 1520 and outputs the values to the decoder 1540.

Specifically, the deinterleaver 1530 is an element corresponding to the interleaver 120 of the transmitting apparatus 100 and performs an operation corresponding to the interleaver 120. That is, the deinterleaver 1530 deinterleaves the LLR value by performing the interleaving operation of the interleaver 120 inversely.

To do so, the deinterleaver 1530 may include a block deinterleaver 1531, a group twist deinterleaver 1532, a group deinterleaver 1533, and a parity deinterleaver 1534 as shown in FIG. 21.

The block deinterleaver 1531 deinterleaves the output of the multiplexer 1520 and outputs a value to the group twist deinterleaver 1532.

Specifically, the block deinterleaver 1531 is an element corresponding to the block interleaver 124 provided in the transmitting apparatus 100 and performs the interleaving operation of the block interleaver 124 inversely.

That is, the block deinterleaver 1531 deinterleaves by writing the LLR value output from the multiplexer 1520 in each row in the row direction and reading each column of the plurality of rows in which the LLR value is written in the column direction by using at least one row formed of the plurality of columns.

In this case, when the block interleaver 124 interleaves by dividing the column into two parts, the block deinterleaver 1531 may deinterleave by dividing the row into two parts.

In addition, when the block interleaver 124 writes and reads in and from the group that does not belong to the first part in the row direction, the block deinterleaver 1531 may deinterleave by writing and reading values corresponding to the group that does not belong to the first part in the row direction.

Hereinafter, the block deinterleaver 1531 will be explained with reference to FIG. 22. However, this is merely an example and the block deinterleaver 1531 may be implemented in other methods.

An input LLR v_(i) (0≤i<N_(ldpc)) is written in a r_(i) row and a c_(i) column of the block deinterleaver 1531. Herein, c_(i)=(i mod N_(c)) and

${r_{i} = \left\lfloor \frac{i}{N_{c}} \right\rfloor},$

On the other hand, an output LLR q_(i)(0≤i<N_(c)×N_(r1)) is read from a c_(i) column and a r_(i) row of the first part of the block deinterleaver 1531. Herein,

${c_{i} = \left\lfloor \frac{i}{N_{r\; 1}} \right\rfloor},$ r_(i)=(i mod N_(r1)).

In addition, an output LLR q₁(N_(c)×N_(r1)≤i<N_(ldpc)) is read from a c_(i) column and a r_(i) row of the second part. Herein,

${c_{i} = \left\lfloor \frac{\left( {i - {N_{c} \times N_{r\; 1}}} \right)}{N_{r\; 2}} \right\rfloor},$ r_(i)=N_(r1)+{(i−N_(c)×N_(r1)) mode N_(r2)}.

The group twist deinterleaver 1532 deinterleaves the output value of the block deinterleaver 1531 and outputs the value to the group deinterleaver 1533.

Specifically, the group twist deinterleaver 1532 is an element corresponding to the group twist interleaver 123 provided in the transmitting apparatus 100, and may perform the interleaving operation of the group twist interleaver 123 inversely.

That is, the group twist deinterleaver 1532 may rearrange the LLR values of the same bit group by changing the order of the LLR values existing in the same bit group. When the group twist operation is not performed in the transmitting apparatus 100, the group twist deinterleaver 1532 may be omitted.

The group deinterleaver 1533 (or the group-wise deinterleaver) deinterleaves an output value of the group twist deinterleaver 1532 and outputs a value to the parity deinterleaver 1534.

Specifically, the group deinterleaver 1533 is an element corresponding to the group interleaver 122 provided in the transmitting apparatus 100 and may perform the interleaving operation of the group interleaver 122 inversely.

That is, the group deinterleaver 1533 may rearrange the order of the plurality of bit groups in bit group wise. In this case, the group deinterleaver 1533 may rearrange the order of the plurality of bit groups in bit group wise by applying the interleaving method of Tables 32 to 56 inversely according to a length of the LDPC codeword, a modulation method and a code rate.

The parity deinterleaver 1534 performs parity deinterleaving with respect to an output value of the group deinterleaver 1533 and outputs a value to the decoder 1540.

Specifically, the parity deinterleaver 1534 is an element corresponding to the parity interleaver 121 provided in the transmitting apparatus 100 and may perform the interleaving operation of the parity interleaver 121 inversely. That is, the parity deinterleaver 1534 may deinterleave the LLR values corresponding to the parity bits from among the LLR values output from the group deinterleaver 1533. In this case, the parity deinterleaver 1534 may deinterleave the LLR value corresponding to the parity bits inversely to the parity interleaving method of Equation 8.

However, the parity deinterleaver 1534 may be omitted depending on the decoding method and embodiment of the decoder 1540.

Although the deinterleaver 1530 of FIG. 20 includes three (3) or four (4) elements as shown in FIG. 21, operations of the elements may be performed by a single element. For example, when bits each of which belongs to each of bit groups X_(a) and X_(b) constitute a single modulation symbol, the deinterleaver 1530 may deinterleave these bits to locations corresponding to their bit groups based on the received single modulation symbol.

For example, when the code rate is 13/15 and the modulation method is QPSK, the group deinterleaver 1533 may perform deinterleaving based on Table 36.

In this case, bits each of which belongs to each of bit groups Y₃(=X₃₈) and Y₂₅(=X₃₇) may constitute a single modulation symbol. Since one bit in each of the bit groups Y₃(=X₃₈) and Y₂₅(=X₃₇) constitutes a single modulation symbol, the deinterleaver 1530 may map bits onto decoding initial values corresponding to the bit groups Y₃(=X₃₈) and Y₂₅(=X₃₇) based on the received single modulation symbol.

The decoder 1540 may perform LDPC decoding by using the output value of the deinterleaver 1530. To achieve this, the decoder 1540 may include an LDPC decoder (not shown) to perform the LDPC decoding.

Specifically, the decoder 1540 is an element corresponding to the encoder 110 of the transmitting apparatus 100 and may correct an error by performing the LDPC decoding by using the LLR value output from the deinterleaver 1530.

For example, the decoder 1540 may perform the LDPC decoding in an iterative decoding method based on a sum-product algorithm. The sum-product algorithm is one example of a message passing algorithm, and the message passing algorithm refers to an algorithm which exchanges messages (e.g., LLR value) through an edge on a bipartite graph, calculates an output message from messages input to variable nodes or check nodes, and updates.

The decoder 1540 may use a parity check matrix when performing the LDPC decoding. In this case, the parity check matrix used in the decoding may have the same configuration as that of the parity check matrix used in the encoding of the encoder 110, and this has been described above with reference to FIGS. 2 to 4.

In addition, information on the parity check matrix and information on the code rate, etc. which are used in the LDPC decoding may be pre-stored in the receiving apparatus 1500 or may be provided by the transmitting apparatus 100.

FIG. 23 is a flowchart to illustrate an interleaving method of a transmitting apparatus according to an exemplary embodiment.

First, an LDPC codeword is generated by LDPC encoding based on a parity check matrix (S1710).

Thereafter, the LDPC codeword is interleaved (S1720). In this case, the LDPC codeword may be interleaved such that bits included in continuous bit groups from among a plurality of bit groups of the LDPC codeword are mapped onto a same modulation symbol. In addition, when there are a plurality of check nodes connected only to a single parity bit in the parity check matrix of the LDPC codeword, the LDPC codeword may be interleaved such that bits included in bit groups corresponding to the parity bit connected to the corresponding check nodes are selectively mapped onto a same modulation symbol.

Then, the interleaved LDPC codeword is mapped onto a modulation symbol (S1730). That is, the bits included in the continuous bit groups from among the plurality of bit groups of the LDPC codeword may be mapped onto a same modulation symbol. In addition, when there are a plurality of check nodes connected only to a single parity bit in the parity check matrix of the LDPC codeword, the bits included in bit groups corresponding to the parity bit connected to the corresponding check nodes may be selectively mapped onto a same modulation symbol.

Each of the plurality of bit groups may be formed of M number of bits, and M may be a common divisor of N_(ldpc) and K_(ldpc) and may be determined to satisfy Q_(ldpc)=(N_(ldpc)−K_(ldpc))/M. Herein, Q_(ldpc) is a cyclic shift parameter value regarding columns in a column group of an information word submatrix of the parity check matrix, N_(ldpc) is a length of the LDPC codeword, and K_(ldpc) is a length of information word bits of the LDPC codeword.

Operation S1720 may include parity-interleaving parity bits of the LDPC codeword, dividing the parity-interleaved LDPC codeword by the plurality of bit groups and rearranging an order of the plurality of bit groups in bit group wise, and interleaving the plurality of bit groups the order of which is rearranged.

The order of the plurality of bit groups may be rearranged in bit group wise based on the above-described Equation 21 presented above.

In Equation 21, π(j) is determined based on at least one of a length of the LDPC codeword and a code rate.

For example, when the LDPC codeword has a length of 16200, the modulation method is QPSK, and the code rate is 13/15, π(j) in Equation 21 may be defined as in Table 36 presented above.

Operation S1720 may include dividing the LDPC codeword by the plurality of bit groups and rearranging an order of the plurality of bit groups in bit group wise, and interleaving the plurality of bit groups the order of which is rearranged.

The order of the plurality of bit groups may be rearranged in bit group wise based on Equation 21 presented above.

π(j) in Equation 21 may be determined based on at least one of a length of the LDPC codeword and a code rate.

For example, when the LDPC codeword has a length of 16200, the modulation method is QPSK, and the code rate is 5/15, π(j) in Equation 21 may be defined as in Table 32 presented above.

However, this is merely an example. The order of the plurality of bit groups may be rearranged in bit group wise by using one of Tables 32 to 56 and Equation 21.

The interleaving the plurality of bit groups may include: writing the plurality of bit groups in each of a plurality of columns in bit group wise in a column direction, and reading each row of the plurality of columns in which the plurality of bit groups are written in bit group wise in a row direction.

In addition, the interleaving the plurality of bit groups may include: serially write, in the plurality of columns, at least some bit group which is writable in the plurality of columns in bit group wise from among the plurality of bit groups, and then dividing and writing the other bit groups in an area which remains after the at least some bit group is written in the plurality of columns in bit group wise.

A non-transitory computer readable medium, which stores a program for performing the interleaving methods according to various exemplary embodiments in sequence, may be provided.

The non-transitory computer readable medium refers to a medium that stores data semi-permanently rather than storing data for a very short time, such as a register, a cache, and a memory, and is readable by an apparatus. Specifically, the above-described various applications or programs may be stored in a non-transitory computer readable medium such as a compact disc (CD), a digital versatile disk (DVD), a hard disk, a Blu-ray disk, a universal serial bus (USB), a memory card, and a read only memory (ROM), and may be provided.

At least one of the components, elements or units represented by a block as illustrated in FIGS. 1, 5, 16, 20 and 21 may be embodied as various numbers of hardware, software and/or firmware structures that execute respective functions described above, according to an exemplary embodiment. For example, at least one of these components, elements or units may use a direct circuit structure, such as a memory, processing, logic, a look-up table, etc. that may execute the respective functions through controls of one or more microprocessors or other control apparatuses. Also, at least one of these components, elements or units may be specifically embodied by a module, a program, or a part of code, which contains one or more executable instructions for performing specified logic functions. Also, at least one of these components, elements or units may further include a processor such as a central processing unit (CPU) that performs the respective functions, a microprocessor, or the like. Further, although a bus is not illustrated in the above block diagrams, communication between the components, elements or units may be performed through the bus. Functional aspects of the above exemplary embodiments may be implemented in algorithms that execute on one or more processors. Furthermore, the components, elements or units represented by a block or processing steps may employ any number of related art techniques for electronics configuration, signal processing and/or control, data processing and the like.

The foregoing exemplary embodiments and advantages are merely exemplary and are not to be construed as limiting the present inventive concept. The exemplary embodiments can be readily applied to other types of apparatuses. Also, the description of the exemplary embodiments is intended to be illustrative, and not to limit the scope of the inventive concept, and many alternatives, modifications, and variations will be apparent to those skilled in the art. 

What is claimed is:
 1. A television (TV) broadcast receiving apparatus comprising: a receiver configured to receive a broadcast signal from a TV broadcast transmitting apparatus; a demodulator configured to demodulate the signal to generate values according to a quadrature phase shift keying (QPSK) modulation; a deinterleaver configured to split the values into a plurality of groups and deinterleave the plurality of groups to provide deinterleaved values; and a decoder configured to decode the deinterleaved values based on a low density parity check (LDPC) code having a code rate being 5/15 and a code length being 16200 bits, wherein the plurality of groups are deinterleaved based on a following equation: Yπ(j)=Xj for (0≤j<N _(group)), where Xj is a jth group among the plurality of groups, Yj is a jth group among the deinterleaved plurality of groups, Ngroup is a total number of the plurality of groups, and π(j) denotes a deinterleaving order for the deinterleaving, and wherein the π(j) is defined as follows: Order of deinterleaving π(j) (0 ≤ j < 45) Code j 0 1 2 3 4 5 6 7 8 9 10 11 Rate 23 24 25 26 27 28 29 30 31 32 33 34 5/15 π(j) 35 7 29 11 14 32 38 28 20 17 25 39 5 13 34 37 23 15 36 18 42 16 33 31 Order of deinterleaving π(j) (0 ≤ j < 45) Code j 12 13 14 15 16 17 18 19 20 21 22 Rate 35 36 37 38 39 40 41 42 43 44 5/15 π(j) 19 4 1 12 10 30 0 44 43 2 21 27 22 3 6 40 24 41 9 26
 8.


2. The receiving apparatus of claim 1, wherein each of the plurality of groups comprises 360 values.
 3. The receiving apparatus of claim 1, wherein π(j) is determined based on at least one of the code length, a modulation method and the code rate. 